5.7 Rational Exponents 5.8 Radical equations

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5.7 Rational Exponents 5.8 Radical equations
Algebra II w/ trig

Rational (fraction) exponents can be rewritten in radical form, and radicals can be rewritten in rational form.

I. Write in radical form. A. B. C. D. E.

II. Write in exponential form. A. B. C. D. E.

III. Evaluate. A. B. C. D.

E. F.

IV. Conditions for a simplified expression
--it has no negative exponents --it has no fractional exponents in denominator --it is not a complex fraction --the index of any remaining radical is small as possible ***if the original problem is in radical form, the answer should be in radical form*** ***If the problem is in rational exponent form, the answer should be in rational form***

A. B.

C. D.

E. F.

5.8 Rational expressions I. Definitions: 1. Radical equations is an equation that has a variable in a radicand. Ex: Not: 2. Extraneous solutions is a solution that does not satisfy the original equation. You can only determine if a solution is extraneous by checking your answer.

II. Steps to Solving Radical Equations:
A. Isolate the radical if possible. B. To eliminate the radical, raise each side of the equation to a power equal to the index of the radical. C. Solve the resulting equation. D. Check for extraneous solutions.

III. Solving a simple radical equation.
A. B.

C. D.

IV. Solving an equation with one radical. A. B.

V. Solving an Equation with two radicals.