# High School Math : Exponents

## Example Questions

### Example Question #1 : Understanding Negative Exponents

Which of the following is equivalent to  ?

Explanation:

By definition,

.

In our problem,  and

Then, we have .

### Example Question #1 : Negative Exponents

Solve for :

Explanation:

Raise both sides of the equation to the inverse power of  to cancel the exponent on the left hand side of the equation.

Subtract  from both sides:

### Example Question #1 : Exponents

Convert the exponent to radical notation.

Explanation:

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

### Example Question #1 : Understanding Fractional Exponents

Which of the following is equivalent to  ?

Explanation:

By definition, a number raised to the  power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

### Example Question #1 : Exponents

Simplify the expression:

Explanation:

Remember that fraction exponents are the same as radicals.

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

Either method, we then need to multiply to two terms.

### Example Question #1 : Simplifying Exponents

Simplify the following expression.

Explanation:

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.

Explanation:

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 #3 : Simplifying Exponents

Simplify the following expression.

Explanation:

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 #1 : Simplifying Exponents

Simplify the following exponent expression:

Explanation:

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: