6.1 Nth Roots and Rational Exponents Objectives: 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?

Concept: Knowing the Parts The index number becomes the denominator of the exponent. Index Number Radical for n > 1 Radicand Exponent The exponent becomes the numerator in Exponential Form

Concept: Radicals If n is odd, then there is one real root. If n is even and a > 0 there are two real roots a = 0 there is one real root a < 0 there are no real roots This is EXACTLY the same as the discriminate we looked at when we used the Quadratic Formula.

Concept: Radical form to Exponential Form Change to exponential form.

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

Concept: Evaluate With a Calculator Rewrite in Exponential Form. 2. Type into calculator

PM 6.1

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

Concept: 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.

Concept: 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.