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# 7.1 - PowerPoint PPT Presentation

7.1/7.2 Nth Roots and Rational Exponents. How do you change a power to rational form and vice versa? How do you evaluate radicals and powers with rational exponents? How do you solve equations involving radicals and powers with rational exponents?. The Nth root. Radical. Index Number.

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### 7.1/7.2 Nth Roots and Rational Exponents

How do you change a power to rational form and vice versa?

How do you evaluate radicals and powers with rational exponents?

How do you solve equations involving radicals and powers with rational exponents?

Index Number

n > 1

The index number becomes the denominator of the exponent.

• If n is odd – one real root.

• If n is even and

• a > 0 Two real roots

• a = 0 One real root

• a < 0 No real roots

Change to exponential form.

or

or

The denominator of the exponent becomes the index number of the radical.

Evaluate without a calculator.

Solve the equation:

Note: index number is even, therefore, two answers.

• Also, Product property for radicals

Simplify.

Example

Simplify.

Note: same index number and same radicand.