High School Math : Distributing Exponents

Example Questions

Example Question #1 : Simplifying Exponents

Solve for .

Possible Answers:

Correct answer:

Explanation:

First, set up the equation: . Simplifying this result gives .

Example Question #1 : Distributing Exponents (Power Rule)

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

Possible Answers:

8

5

10

16

20

Correct answer:

16

Explanation:

. Thus,  is equal to 16.

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

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: