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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?

The Nth root Radical Index Number n > 1
The index number becomes the denominator of the exponent. Radicand

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

Example: Radical form to Exponential Form
Change to exponential form. or or

Example: Exponential to Radical Form
Change to radical form. The denominator of the exponent becomes the index number of the radical.

Example: Evaluate Without a Calculator

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

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

Example: Using the Quotient Property
Simplify.

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.

Example: Addition with like radicals
Simplify. Note: same index number and same radicand. Add the coefficients.

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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