Lesson 8-6B Use Cube Roots and Fractional Exponents

After today’s lesson, you should be able to evaluate cube roots and simplify expressions

with fractional exponents. (CA Alg 2.0)

Finding cube roots: Fractional Exponents (also called Rational Exponents)

We have used radical signs to write square roots and cube roots. We can also write square roots and cube roots using fractional exponents.

Cube Roots

As opposed to writing cube roots using the radical symbol , we can instead use an exponent of .Example:

or

Square Roots

As opposed to writing square roots with the radical symbol we can use an exponent of Example:

or

The Rule

The rule for fractional exponents is that the numerator of the exponent is the power and the denominator is the root.

***The root of the base must be found before we can apply the power.

The Rule

Consider The base is 16, the power is 3, and the root is 2.

This means that can be rewritten as

Examples: Rewrite using radical notation.

1)

Examples: Rewrite using radical notation.

2)

Examples: Rewrite using radical notation.

3) You Try

You can also use fractional exponents when raising a radical to a power:

4)

You can also use fractional exponents when raising a radical to a power:

5)

You can also use fractional exponents when raising a radical to a power:

6) You Try

You can reverse this process to rewrite expressions containing fractional exponents into

radical form.7)

You can reverse this process to rewrite expressions containing fractional exponents into

radical form.8)

You can reverse this process to rewrite expressions containing fractional exponents into

radical form.9) You Try

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.10)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.11)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.12)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.13) You Try

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.14)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.15)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.16)

We can now evaluate expressions containing rational exponents.

Examples: Evaluate.17) You Try