### All High School Math Resources

## Example Questions

### Example Question #1 : Simplifying Exponents

Solve for .

**Possible Answers:**

**Correct answer:**

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

. Thus, is equal to 16.

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

Order the following from least to greatest:

**Possible Answers:**

**Correct answer:**

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 : Integer Exponents

Simplify the expression:

**Possible Answers:**

Cannot be simplified

**Correct answer:**

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:

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