# Algebra II : Distributing Exponents (Power Rule)

## Example Questions

← Previous 1 3 4 5 6 7 8 9 12 13

### Example Question #1 : Distributing Exponents (Power Rule)

What is the largest positive integer, , such that is a factor of ?

Possible Answers:

5

8

10

20

16

Correct answer:

16

Explanation: . Thus, is equal to 16.

### Example Question #1 : Integer Exponents

Simplify the expression: Possible Answers:    Cannot be simplified

Correct answer: Explanation:

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied: Any negative exponents can be converted to positive exponents in the denominator of a fraction: The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:  ### Example Question #2 : Distributing Exponents (Power Rule)

Order the following from least to greatest:     Possible Answers:     Correct answer: Explanation:

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent.  Then they can be easily compared.  , , and .

Thus, ordering from least to greatest: .

### Example Question #3 : Distributing Exponents (Power Rule)

Simplify: Possible Answers:     Correct answer: Explanation: Step 1: Distribute the exponents in the numberator. Step 2: Represent the negative exponents in the demoninator. Step 3: Simplify by combining terms.  ### Example Question #2 : Integer Exponents

Simplify: Possible Answers:     Correct answer: Explanation:

Use the power rule to distribute the exponent: ### Example Question #4 : Distributing Exponents (Power Rule)

Simplify: Possible Answers:     Correct answer: Explanation:

Step 1: Distribute the exponent through the terms in parentheses: Step 2: Use the division of exponents rule.  Subtract the exponents in the numerator from the exponents in the denominator: ### Example Question #5 : Distributing Exponents (Power Rule)

Simplify. Possible Answers:     Correct answer: Explanation:

When a power applies to an exponent, it acts as a multiplier, so 2a becomes 4a and -b becomes -2b. The negative exponent is moved to the denominator.

### Example Question #6 : Distributing Exponents (Power Rule)

Simplify .

Possible Answers:     Correct answer: Explanation:

When faced with a problem that has an exponent raised to another exponent, the powers are multiplied: then simplify: .

### Example Question #7 : Distributing Exponents (Power Rule)

Solve: Possible Answers:     Correct answer: Explanation:

Solve each term separately.  A number to the zeroth power is equal to 1, but be careful to apply the signs after the terms have been simplified. ### Example Question #8 : Distributing Exponents (Power Rule)

Simplify this expression: Possible Answers:     Correct answer: Explanation: is the correct answer because the order of operations were followed and the multiplication and power rules of exponents were obeyed. These rules are as follows: PEMDAS (parentheses,exponents, multiplication, division, addition, subtraction), for multiplication of exponents follow the format , and . First we simplify terms within the parenthesis because of the order of operations and the multiplication rule of exponents: Next we use the power rule to distribute the outer power: = **note that in the first step it isn't necessary to combine the two x powers because the individuals terms will still add to x^16 at the end if you use the power rule correctly. However, following the order of operations is a great way to avoid simple math errors and is relevant in many problems.

← Previous 1 3 4 5 6 7 8 9 12 13

### All Algebra II Resources 