6-3: Rational Exponents Unit 6: Rational /Radical Equations

Recall: Exponent Rules Rational exponents behave exactly like the whole number exponents

Let’s look at some review problems

Definition of a rational exponent

Roots of nth roots CaseRootsExample Odd index1 real root Even index (positive radicand) 2 real roots Even index (negative radicand) No real roots radicand of 01 root of 0

Find all real roots

Simplifying nth roots Recall: and The same applies here: Ex.

Definition of a rational exponent A rational exponent is defined as: Where m and n are integers and n ≠ 0. Ex.

Write each expression in radical form and simplify. Write each expression using rational exponents. Solve.