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Rational Exponents

• Definition of If n is a positive integer greater than 1 and is a real number , then

Rewrite as a radical expression and simplify if possible.

• Definition of If m and n are positive integers greater than 1 with in simplest form , then

as long as is a real number .

Use radical notation to rewrite each expression. Simplify if possible.

• Definition of as long as is a nonzero real number .

Write each expression with a positive exponent . Then simplify.

Summary of Exponent Rules
If m and n are rational numbers , and a, b, and c are numbers for which the expressions below exist,
then
Product rule for exponents:

Power rule for exponents :

Power rules for products and quotients:

Quotient rule for exponents :

Zero exponent :

Negative exponent :

Use the properties of exponents to simplify.

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