### All High School Math Resources

## Example Questions

### Example Question #1 : Simplifying Exponents

Simplify the following expression.

**Possible Answers:**

**Correct answer:**

When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: .

In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.

Now, simplifly the numerals.

### Example Question #2 : Simplifying Exponents

Simplify the following expression.

**Possible Answers:**

**Correct answer:**

We are given: .

Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.

Thus, we have .

### Example Question #1 : Simplifying Exponents

Simplify the following expression.

**Possible Answers:**

**Correct answer:**

Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.

Thus, we have .

We also recall that for negative exponents,

.

Thus, .

### Example Question #4 : Simplifying Exponents

Simplify the following exponent expression:

**Possible Answers:**

**Correct answer:**

Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:

Multiply the exponents:

Simplify:

### Example Question #5 : Simplifying Exponents

Simplify the expression:

**Possible Answers:**

**Correct answer:**

First simplify the second term, and then combine the two:

### Example Question #6 : Simplifying Exponents

Solve for :

**Possible Answers:**

Cannot be determined from the given information.

**Correct answer:**

Rewrite each side of the equation to only use a base 2:

The only way this equation can be true is if the exponents are equal.

So:

The on each side cancel, and moving the to the left side, we get:

### Example Question #7 : Simplifying Exponents

Solve for .

**Possible Answers:**

**Correct answer:**

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

### Example Question #8 : Simplifying Exponents

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

**Possible Answers:**

8

10

16

5

20

**Correct answer:**

16

. Thus, is equal to 16.

### Example Question #9 : Simplifying Exponents

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 #10 : Simplifying 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: