### Which Law Would You Use To Simplify The Expression?

- Marvin Harvey
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Simplify to form an equivalent expression by combining like terms. Use the distributive law as needed. p-3 p 00:41 Simplify to form an equivalent expression by combining like terms. Use the distributive law as needed.

## What rule should be used to simplify the expression?

How to Simplify Expressions? – Before learning about simplifying expressions, let us quickly go through the meaning of expressions in math. Expressions refer to mathematical statements having a minimum of two terms containing either numbers, variables, or both connected through an addition/subtraction operator in between.

- The general rule to simplify expressions is PEMDAS – stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- In this article, we will be focussing more on how to simplify algebraic expressions.
- Let’s begin! We need to learn how to simplify expressions as it allows us to work more efficiently with algebraic expressions and ease out our calculations.

To simplify algebraic expressions, follow the steps given below:

- Step 1: Solve parentheses by adding/subtracting like terms inside and by multiplying the terms inside the brackets with the factor written outside. For example, 2x (x + y) can be simplified as 2x 2 + 2xy.
- Step 2: Use the exponent rules to simplify terms containing exponents,
- Step 3: Add or subtract the like terms.
- Step 4: At last, write the expression obtained in the standard form (from highest power to the lowest power).

Let us take an example for a better understanding. Simplify the expression: x (6 – x) – x (3 – x). Here, there are two parentheses both having two unlike terms. So, we will be solving the brackets first by multiplying x to the terms written inside. x(6 – x) can be simplified as 6x – x 2, and -x(3 – x) can be simplified as -3x + x 2,

Now, combining all the terms will result in 6x – x 2 – 3x + x 2, In this expression, 6x and -3x are like terms, and -x 2 and x 2 are like terms. So, adding these two pairs of like terms will result in (6x – 3x) + (-x 2 + x 2 ). By simplifying it further, we will get 3x, which will be the final answer.

Therefore, x (6 – x) – x (3 – x) = 3x. Look at the image given below showing another simplifying expression example.

### Which law would you use to simplify the expression product of powers?

A – The power of power rule states that when a number with an exponent is raised to another exponent, the expression can be simplified by keeping the base and multiplying the exponents. The general form of the rule is \((a^m)^n=a^ \). We can see why the rule works by expanding the exponents.

## Which law would use to simplify the expression 3 10 3 4?

Use the distributive law as needed.

## Which expression is equivalent to 5 10?

Related Articles – Two or more fractions that have different numerators and denominators but result in the same value after simplification are said to be equivalent fractions. The examples of equivalent fractions are: 2/4 and 3/6 ⅓ and 3/9 ⅕ and 5/25 ¾ and 12/16 We need to simplify the given fractions to find whether they are equivalent or not.

Suppose 3/9 and ⅔ are two fractions.3/9 can be further simplified to ⅓, but ⅓ is not equal to ⅔. Therefore, they are not equivalent. But, ⅚ and 10/12 are equivalent fractions because 10/12 = ⅚. To find the equivalent fraction of ⅗, we need to multiply both numerator and denominator by the same number. Hence, ⅗ × (2/2) = 6/10 5/10 is equal to ½ after simplification.

Hence, the equivalent fractions of 5/10 are: ½, 2/4, 3/6, 4/8 and so on. : Equivalent Fractions – Definition, How to Find Equivalent Fractions, Examples

## What is the simplified of the expression?

To simplify a mathematical expression is to represent it in the least complicated form possible. In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

## What law of exponents is simplified?

Simplify by Using the Product, Quotient, and Power Rules

- Simplify by Using the Product, Quotient, and Power Rules
- Learning Objective(s)
- · Use the product rule to multiply exponential expressions with like bases.
- · Use the power rule to raise powers to powers.
- · Use the quotient rule to divide exponential expressions with like bases.
- · Simplify expressions using a combination of the properties,

was developed to write repeated multiplication more efficiently. There are times when it is easier to leave the expressions in exponential notation when multiplying or dividing. Let’s look at rules that will allow you to do this. The Product Rule for Exponents Recall that exponents are a way of representing repeated multiplication.

For example, the notation 5 4 can be expanded and written as 5 • 5 • 5 • 5, or 625. And don’t forget, the exponent only applies to the number immediately to its left, unless there are parentheses. What happens if you multiply two numbers in exponential form with the same base? Consider the expression (2 3 )(2 4 ).

Expanding each exponent, this can be rewritten as (2 • 2 • 2) (2 • 2 • 2 • 2) or 2 • 2 • 2 • 2 • 2 • 2 • 2. In exponential form, you would write the product as 2 7, Notice, 7 is the sum of the original two exponents, 3 and 4. What about ( x 2 )( x 6 )? This can be written as ( x • x )( x • x • x • x • x • x ) = x • x • x • x • x • x • x • x or x 8,

The For any number x and any integers a and b, ( x a )( x b ) = x a + b, |

To multiply exponential terms with the same base, simply add the exponents.

Example | ||

Problem | Simplify. ( a 3 )( a 7 ) | |

( a 3 )( a 7 ) | The base of both exponents is a, so the product rule applies. | |

a 3+7 | Add the exponents with a common base. | |

( a 3 )( a 7 ) = a 10 |

When multiplying more complicated terms, multiply the coefficients and then multiply the variables.

Example | ||

Simplify.5 a 4 · 7 a 6 | ||

35 · a 4 · a 6 | Multiply the coefficients. | |

35 · a 4+6 | The base of both exponents is a, so the product rule applies. Add the exponents. | |

35 · a 10 | Add the exponents with a common base. | |

Answer | 5 a 4 · 7 a 6 = 35 a 10 |

table>

- Simplify the expression, keeping the answer in exponential notation.
- (4 x 5 )( 2 x 8 )
- A) 8 x 5 • x 8
- B) 6 x 13
- C) 8 x 13
- D) 8 x 40

A) 8 x 5 • x 8 Incorrect.8 x 5 • x 8 is equivalent to (4 x 5 )(2 x 8 ), but it still is not in simplest form. Simplify x 5 • x 8 by using the Product Rule to add exponents. The correct answer is 8 x 13, B) 6 x 13 Incorrect.6 x 13 is not equivalent to (4 x 5 )(2 x 8 ). In this incorrect response, the correct exponents were added, but the coefficients were also added together. They should have been multiplied. The correct answer is 8 x 13, C) 8 x 13 Correct.8 x 13 is equivalent to (4 x 5 )(2 x 8 ). Multiply the coefficients (4 • 2) and apply the Product Rule to add the exponents of the variables (in this case x ) that are the same. D) 8 x 40 Incorrect.8 x 40 is not equivalent to (4 x 5 )(2 x 8 ). Do not multiply the coefficients and the exponents. Remember, using the Product Rule add the exponents when the bases are the same. The correct answer is 8 x 13,

The Power Rule for Exponents Let’s simplify (5 2 ) 4, In this case, the base is 5 2 and the exponent is 4, so you multiply 5 2 four times: (5 2 ) 4 = 5 2 • 5 2 • 5 2 • 5 2 = 5 8 (using the Product Rule – add the exponents). (5 2 ) 4 is a power of a power.

- It is the fourth power of 5 to the second power.
- And we saw above that the answer is 5 8,
- Notice that the new exponent is the same as the product of the original exponents: 2 • 4 = 8.
- So, (5 2 ) 4 = 5 2 • 4 = 5 8 (which equals 390,625, if you do the multiplication).
- Likewise, ( x 4 ) 3 = x 4 • 3 = x 12,

This leads to another rule for exponents—the, To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (2 3 ) 5 = 2 15,

The Power Rule for Exponents For any positive number x and integers a and b : ( x a ) b = x a · b, |

table>

Example Problem Simplify.6( c 4 ) 2 6( c 4 ) 2 Since you are raising a power to a power, apply the Power Rule and multiply exponents to simplify. The coefficient remains unchanged because it is outside of the parentheses. Answer 6( c 4 ) 2 = 6 c 8table>

Example Problem Simplify. a 2 ( a 5 ) 3 Raise a 5 to the power of 3 by multiplying the exponents together (the Power Rule). Since the exponents share the same base, a, they can be combined (the Product Rule). Answertable>

- Simplify:
- A)
- B)
- C)
- D)

A) Incorrect. This expression is not simplified yet. Recall that – a can also be written – a 1, Multiply – a 1 by a 8 to arrive at the correct answer. The correct answer is, B) Incorrect. Do not add the exponents of 2 and 4 together. The Power Rule states that for a power of a power you multiply the exponents.,

The Quotient Rule for Exponents Let’s look at dividing terms containing exponential expressions. What happens if you divide two numbers in exponential form with the same base? Consider the following expression. You can rewrite the expression as:, Then you can cancel the common factors of 4 in the numerator and denominator: Finally, this expression can be rewritten as 4 3 using exponential notation. Notice that the exponent, 3, is the difference between the two exponents in the original expression, 5 and 2.

- So, = 4 5-2 = 4 3,
- Be careful that you subtract the exponent in the denominator from the exponent in the numerator.
- or
- = x 7 − 9 = x -2
- So, to divide two exponential terms with the same base, subtract the exponents.

Notice that = 4 0, And we know that = = 1. So this may help to explain why 4 0 = 1.

Example | ||

Problem | Evaluate. | |

These two exponents have the same base, 4. According to the Quotient Rule, you can subtract the power in the denominator from the power in the numerator. | ||

= 4 5 |

When dividing terms that also contain coefficients, divide the coefficients and then divide variable powers with the same base by subtracting the exponents.

Example | ||

Problem | Simplify. | |

Separate into numerical and variable factors. | ||

Since the bases of the exponents are the same, you can apply the Quotient Rule. Divide the coefficients and subtract the exponents of matching variables. | ||

Answer | = |

All of these rules of exponents—the Product Rule, the Power Rule, and the Quotient Rule—are helpful when evaluating expressions with common bases.

Example | ||

Problem | Evaluate when x = 4. | |

Separate into numerical and variable factors. | ||

Divide coefficients, and subtract the exponents of the variables. | ||

Simplify. | ||

Substitute the value 4 for the variable x, | ||

Answer | = 768 |

Usually, it is easier to simplify the expression before substituting any values for your variables, but you will get the same answer either way.

Example | ||

Problem | Simplify. | |

Use the order of operations with PEMDAS: E: Evaluate exponents. Use the Power Rule to simplify (a 5 ) 3, | ||

M: Multiply, using the Product Rule as the bases are the same. | ||

D: Divide using the Quotient Rule. | ||

= |

There are rules that help when multiplying and dividing exponential expressions with the same base. To multiply two exponential terms with the same base, add their exponents. To raise a power to a power, multiply the exponents. To divide two exponential terms with the same base, subtract the exponents. : Simplify by Using the Product, Quotient, and Power Rules

#### What is freedom of expression in law?

Freedom of expression and information – Freedom of Expression You have the right to seek, receive and impart information and ideas of your choice without interference and regardless of frontiers, This means: You have the freedom to express yourself online and to access information and the opinions and expressions of others.

- This includes political speech, views on religion, opinions and expressions that are favourably received or regarded as inoffensive, but also those that may offend, shock or disturb others.
- You should have due regard to the reputation or rights of others, including their right to privacy.
- Restrictions may apply to expressions which incite discrimination, hatred or violence,

These restrictions must be lawful, narrowly tailored and executed with court oversight. You are free to create, re-use and distribute content respecting the right to protection of intellectual property, including copyright. Public authorities have a duty to respect and protect your freedom of expression and your freedom of information,

Any restrictions to this freedom must not be arbitrary, must pursue a legitimate aim in accordance with the European Convention on Human Rights such as, among others, the protection of national security or public order, public health or morals, and must comply with human rights law. Moreover, they must be made known to you, coupled with information on ways to seek guidance and redress, and not be broader or maintained for longer than is strictly necessary to achieve a legitimate aim.

Your Internet service provider and your provider of online content and services have corporate responsibilities to respect your human rights and provide mechanisms to respond to your claims, You should be aware, however, that online service providers, such as social networks, may restrict certain types of content and behaviour due to their content policies.

You should be informed of possible restrictions so that you are able to take an informed decision as to whether to use the service or not. This includes specific information on what the online service provider considers as illegal or inappropriate content and behaviour when using the service and how it is dealt with by the provider.

You may choose not to disclose your identity online, for instance by using a pseudonym. However, you should be aware that measures can be taken, by national authorities, which might lead to your identity being revealed. : Freedom of expression and information – Freedom of Expression

### Which property of exponents is used to simplify the expression?

To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator. Since 9>7, there are more factors of x in the numerator. Use Quotient Property, aman=am−n.

## What law of Radical Will you apply to simplify the expression?

Summary – A radical expression is a mathematical way of representing the n th root of a number. Square roots and cube roots are the most common radicals, but a root can be any number. To simplify radical expressions, look for exponential factors within the radical, and then use the property \sqrt ^ }}=x if n is odd and \sqrt ^ }}=\left| x \right| if n is even to pull out quantities.

### What is the correct answer to 2 5 * 4 8 4 ⁄ 5?

= 12. Was this answer helpful?

### What is this expression in simplified form square root of 22?

Square Root of 22 by Long Division Method – To find the square root of 22 by long division,

- Step 1: Write the pair of digits starting from one’s place. Here 22 is the pair to be taken.
- Step 2 : Find a divisor ‘n’ such that n × n results in a product that is less than or equal to 22. We know that 4 × 4 = 16
- Step 3 : Find the difference as done in the usual division. (22-16= 6). Double the quotient that was calculated.4 × 2 and write it in the new divisor’s place. Here it’s 8. We leave a blank to create a new divisor.
- Step 4 : Here we have no other numbers to divide, So, we keep a decimal point after the dividend 22 and quotient 4. Now, place 2 pairs of zeros after the decimal of the dividend. Bring the pair of zeros down.
- Step 5 : Find a divisor ‘n’ such that n × n results in a product that is less than or equal to 600. Write the next quotient as 6. Now we get our new divisor as 86, as 6 × 86 = 516. Do the division and get the remainder, Here we get 84
- Step 6 : Bring the next pair of zeros down.
- Step 7: Double the quotient 46. (2 × 46 = 92). Write it in the new divisor’s place and leave a blank next to it.
- Step 8: Find a divisor ‘n’ such that n × n results in a product that is less than or equal to 8400. We find that 9 × 929= 8361. We can stop here as we have found the quotient up to 2 decimal places.

Thus, √ 22 = 4.69 by long division. We might proceed further to get the answer to further decimal places. Explore Square roots using illustrations and interactive examples

- Square Root of 25
- Square Root of 24
- Square Root of 28
- Square Root of 225
- Square Root of 45

Important Notes:

- We can find the actual value of √ 22= 4.69041575982343 by the long division method.
- The square root of 22 is already in its simplest radical form and cannot be simplified.

Challenging Questions:

- What is the value of √ √ 22?
- Can you think of any quadratic equation which has a root as √ 22?

- Example 1 : Sam wants to paint a square wall that has an area of 22 feet 2, What is the length of the side of the square wall? Solution Area of the square wall = 22 feet 2 We know that area of a square is: (side × side) square sq units Side² = 22 Thus, side = √ 22 Side= 4.69 feet Hence, the length of the side of the square wall= 4.69 feet
- Example 2 : Help James find the two consecutive numbers between which the square root of 22 lies. Solution James knows that the perfect squares nearest to 22 are 16 and 25 The square root of 16 is 4 The square root of 25 is 5 These are the two numbers between which the square root of 22 lies. Hence, James found that the square root of 22 lies between 16 and 25
- Example: If the area of an equilateral triangle is 22√3 in 2, Find the length of one of the sides of the triangle. Solution: Let ‘a’ be the length of one of the sides of the equilateral triangle. ⇒ Area of the equilateral triangle = (√3/4)a 2 = 22√3 in 2 ⇒ a = ±√88 in Since length can’t be negative, ⇒ a = √88 = 2 √22 We know that the square root of 22 is 4.690. ⇒ a = 9.381 in

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### What is 3 4 equal to in fractions?

Decimal and Fraction Conversion Chart –

Fraction | Equivalent Fractions | Decimal | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 6/12 | 7/14 | 8/16 | 9/18 | 10/20 | 11/22 | 12/24 | .5 |

1/3 | 2/6 | 3/9 | 4/12 | 5/15 | 6/18 | 7/21 | 8/24 | 9/27 | 10/30 | 11/33 | 12/36 | .333 |

2/3 | 4/6 | 6/9 | 8/12 | 10/15 | 12/18 | 14/21 | 16/24 | 18/27 | 20/30 | 22/33 | 24/36 | .666 |

1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 6/24 | 7/28 | 8/32 | 9/36 | 10/40 | 11/44 | 12/48 | .25 |

3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 18/24 | 21/28 | 24/32 | 27/36 | 30/40 | 33/44 | 36/48 | .75 |

1/5 | 2/10 | 3/15 | 4/20 | 5/25 | 6/30 | 7/35 | 8/40 | 9/45 | 10/50 | 11/55 | 12/60 | .2 |

2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 12/30 | 14/35 | 16/40 | 18/45 | 20/50 | 22/55 | 24/60 | .4 |

3/5 | 6/10 | 9/15 | 12/20 | 15/25 | 18/30 | 21/35 | 24/40 | 27/45 | 30/50 | 33/55 | 36/60 | .6 |

4/5 | 8/10 | 12/15 | 16/20 | 20/25 | 24/30 | 28/35 | 32/40 | 36/45 | 40/50 | 44/55 | 48/60 | .8 |

1/6 | 2/12 | 3/18 | 4/24 | 5/30 | 6/36 | 7/42 | 8/48 | 9/54 | 10/60 | 11/66 | 12/72 | .166 |

5/6 | 10/12 | 15/18 | 20/24 | 25/30 | 30/36 | 35/42 | 40/48 | 45/54 | 50/60 | 55/66 | 60/72 | .833 |

1/7 | 2/14 | 3/21 | 4/28 | 5/35 | 6/42 | 7/49 | 8/56 | 9/63 | 10/70 | 11/77 | 12/84 | .143 |

2/7 | 4/14 | 6/21 | 8/28 | 10/35 | 12/42 | 14/49 | 16/56 | 18/63 | 20/70 | 22/77 | 24/84 | .286 |

3/7 | 6/14 | 9/21 | 12/28 | 15/35 | 18/42 | 21/49 | 24/56 | 27/63 | 30/70 | 33/77 | 36/84 | .429 |

4/7 | 8/14 | 12/21 | 16/28 | 20/35 | 24/42 | 28/49 | 32/56 | 36/63 | 40/70 | 44/77 | 48/84 | .571 |

5/7 | 10/14 | 15/21 | 20/28 | 25/35 | 30/42 | 35/49 | 40/56 | 45/63 | 50/70 | 55/77 | 60/84 | .714 |

6/7 | 12/14 | 18/21 | 24/28 | 30/35 | 36/42 | 42/49 | 48/56 | 54/63 | 60/70 | 66/77 | 72/84 | .857 |

1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 6/48 | 7/56 | 8/64 | 9/72 | 10/80 | 11/88 | 12/96 | .125 |

3/8 | 6/16 | 9/24 | 12/32 | 15/40 | 18/48 | 21/56 | 24/64 | 27/72 | 30/80 | 33/88 | 36/96 | .375 |

5/8 | 10/16 | 15/24 | 20/32 | 25/40 | 30/48 | 35/56 | 40/64 | 45/72 | 50/80 | 55/88 | 60/96 | .625 |

7/8 | 14/16 | 21/24 | 28/32 | 35/40 | 42/48 | 49/56 | 56/64 | 63/72 | 70/80 | 77/88 | 84/96 | .875 |

1/9 | 2/18 | 3/27 | 4/36 | 5/45 | 6/54 | 7/63 | 8/72 | 9/81 | 10/90 | 11/99 | 12/108 | .111 |

2/9 | 4/18 | 6/27 | 8/36 | 10/45 | 12/54 | 14/63 | 16/72 | 18/81 | 20/90 | 22/99 | 24/108 | .222 |

4/9 | 8/18 | 12/27 | 16/36 | 20/45 | 24/54 | 28/63 | 32/72 | 36/81 | 40/90 | 44/99 | 48/108 | .444 |

5/9 | 10/18 | 15/27 | 20/36 | 25/45 | 30/54 | 35/63 | 40/72 | 45/81 | 50/90 | 55/99 | 60/108 | .555 |

7/9 | 14/18 | 21/27 | 28/36 | 35/45 | 42/54 | 49/63 | 56/72 | 63/81 | 70/90 | 77/99 | 84/108 | .777 |

8/9 | 16/18 | 24/27 | 32/36 | 40/45 | 48/54 | 56/63 | 64/72 | 72/81 | 80/90 | 88/99 | 96/108 | .888 |

## What is the first step to simplifying an expression?

The first step in simplifying a rational expression is to determine the domainThe set of all possible inputs of a function which allow the function to work., the set of all possible values of the variables.

#### What is the rule of expression?

Docs Home → Atlas App Services A rule expression is a JSON object that you write to control data access with rules, Each expression defines the conditions under which a user can take some action. For example, you can write an expression to control whether a user can read or write data in a MongoDB document or a synced realm.

- When Atlas App Services evaluates a rule, it resolves each expression associated with the rule to a boolean value, either true or false,
- You can define simple, static expressions that use hardcoded values: A “static” expression that only matches the hardcoded ID You can also write expressions that support arbitrary logic to express dynamic requirements and complex or custom workflows.

A dynamic expression can include variables that reflect the current context, called expansions, and can use built-in operators to transform data: A “dynamic” expression that varies based on the requesting user and their IP location

} |

An expression is either a boolean value (i.e. true or false ) or a JSON object. Expression object field names can be a value, an expansion, or an operator, Each field must contain one of a value, an expansion, or a nested expression. Expression object have the following format:

You can embed multiple expression documents in the fields of another expression document to handle complex evaluation logic. App Services evaluates expressions depth-first, post-order, i.e. it starts at the bottom of the expression tree and works back to the root-level fields by evaluating each expression after all of its embedded expressions.

## Which rule is used to solve expression equations?

What exactly is BODMAS? – BODMAS is a set of rules or an order to perform an arithmetic expression so that evaluation becomes easier. Mathematics is all about logic and certain rules are mandatory to be followed. BODMAS is one of them which if not followed the whole answer can go wrong and end up in losing the marks unnecessarily.

BODMAS can be further defined as standard rules for simplifying the expression having multiple operators. Athematic expressions have mainly two components that are Numbers and operators: Numbers are the values for making calculations and representing the quantities. There are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers.

The Operators is the combination of two characters that form an expression or the equation. The most common are addition, multiplication. Division and subtraction. Any expression having just one operator, the solving becomes easy but when there are multiple operators it becomes a little tough.

- For example:
- See the equation (3+4)5+6-2
- According to BODMAS:

- The first step is to add the numerical that is in the bracket that is 3+4=7
- The next step is to multiply 7 with 5=7×5=35
- The next step is to add 35+6=41
- Then subtract 2 that is 41-2=39

Whenever an equation is involved with bracket, addition, subtraction BODMAS has to be followed. This acronym is created so that it is easier to remember.