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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?

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**The Nth root Radical Index Number n > 1**

The index number becomes the denominator of the exponent. Radicand

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**Radicals If n is odd – one real root. If n is even and**

a > Two real roots a = One real root a < No real roots

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**Example: Radical form to Exponential Form**

Change to exponential form. or or

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**Example: Exponential to Radical Form**

Change to radical form. The denominator of the exponent becomes the index number of the radical.

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**Example: Evaluate Without a Calculator**

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**Example: Solving an equation**

Solve the equation: Note: index number is even, therefore, two answers.

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Rules Rational exponents and radicals follow the properties of exponents. Also, Product property for radicals Quotient property for radicals

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**Example: Using the Quotient Property**

Simplify.

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**Adding and Subtracting Radicals**

Two radicals are like radicals, if they have the same index number and radicand Example Addition and subtraction is done with like radicals.

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**Example: Addition with like radicals**

Simplify. Note: same index number and same radicand. Add the coefficients.

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**Example: Subtraction Simplify.**

Note: The radicands are not the same. Check to see if we can change one or both to the same radicand. Note: The radicands are the same. Subtract coefficients.

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