# Rational Exponents Fraction Exponents.

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Rational Exponents Fraction Exponents

By definition of Radical Expression. The index of the Radical is 3.

How would we simplify this expression?
What does the fraction exponent do to the number? The number can be written as a Radical expression, with an index of the denominator.

The Rule for Rational Exponents

Write each Radical using Rational Exponents

Write each Radical using Rational Exponents

Negative exponents make inverses.

What if the numerator is not 1 Always remember:
Evaluate

What if the numerator is not 1
Evaluate

What if the numerator is not 1
Evaluate

For any nonzero real number b, and integer m and n
Make sure the Radical express is real, no b<0 when n is even.

Simplify each expression
No fraction in the denominators.

Simplify each expression
No fraction in the denominators.

Simplify

Simplify

Simplify

Simplifying exponential expressions
If in radical form, transform to exponential form Simplify by applying the exponent to each base. Express with positive exponents or radical form, depending on the directions

Express in simplest form
Make exponential first!

Express in simplest form
Make exponential first! Now simplify

Express in simplest form
Make exponential first! Now simplify

Next example Use positive exponents only!

Next example Use positive exponents only! Or in radical form:

Simplify

Simplify

Simplify

Simplify