Suppose you want to find the cube root of a number, but your calculator only allows you to find square roots. However, it does allow you to find a number raised to any power, including non-integer powers. What would you do? Is there a way that you could rewrite the cube root of a number with a fractional exponent so that you could use your calculator to find the answer?

### Fractional Exponents

The next objective is to be able to use fractions as exponents in an expression.

You can write roots as fractional exponents using the rule .

#### Let's simplify the following expressions by writing them without a root:

#### Evaluating Expressions with Exponents

It is important when evaluating expressions that you remember the Order of Operations. Evaluate what is inside the parentheses, then evaluate the exponents, then perform multiplication/division from left to right, and then perform addition/subtraction from left to right.

#### Let's evaluate the following expression:

### Examples

#### Example 1

Earlier, you were asked how you can write the cube root so that you can use your calculator to find cube root of a number.

As shown in this concept, you can write a root as a fractional exponent where the denominator is the power of the root and the numerator is the power that is inside the root.

A cube root can be written as the number to the power.

#### Example 2

Simplify .

We start by simplifying using the fact that .

Next we rearrange knowing that 6 and 2 have a common factor, 2.

### Review

Simplify the following expressions. Be sure the final answer includes only positive exponents.

Simplify the following expressions without any fractions in the answer.

Evaluate the following expressions to a single number.

**Mixed Review**

- A quiz has ten questions: 7 true/false and 3 multiple choice. The multiple choice questions each have four options. How many ways can the test be answered?
- Simplify .
- Simplify .
- Simplify .
- Solve for .

### Review (Answers)

To view the Review answers, open this PDF file and look for section 8.4.