### 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 #1 : 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 : Multiplying And Dividing 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 #1 : Simplifying Exponents

Simplify the expression:

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : 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: