Nth roots and Rational Exponents Section 5.1 6/26/2018 5:52 AM

DEFINITIONS EXPONENT BASE Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power EXPONENT BASE 6/26/2018 5:52 AM

THE EXPONENT 6/26/2018 5:52 AM

NTH ROOT RULE M is the power (exponent) N is the root A is the base 6/26/2018 5:52 AM

RULES Another way of writing is 251/2. is written in radical expression form. 251/2 is written in rational exponent form. Why is square root of 25 equals out of 25 raised to ½ power? 6/26/2018 5:52 AM

EXAMPLE 1 Evaluate 43/2 in radical form and simplify.

Evaluate 43/2 in radical form and simplify. EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 6/26/2018 5:52 AM 10.2 - Rational Exponents

EXAMPLE 2 Evaluate 41/2 in radical form and simplify.

YOUR TURN Evaluate (–27)2/3 in radical form and simplify. 6/26/2018 5:52 AM

EXAMPLE 3 Evaluate –274/3 in radical form and simplify. Use calculator to check Hint: Remember, the negative is OUTSIDE of the base 6/26/2018 5:52 AM

EXAMPLE 4 Evaluate in radical form and simplify. 6/26/2018 5:52 AM

NTH ROOT RULE M is the power (exponent) N is the root A is the base   M is the power (exponent) N is the root A is the base 6/26/2018 5:52 AM 10.2 - Rational Exponents

EXAMPLE 5 Evaluate (27)–2/3 in radical form and simplify. 10.2 - Rational Exponents

EXAMPLE 6 Evaluate (–64)–2/3 in radical form and simplify. 10.2 - Rational Exponents

YOUR TURN Evaluate in radical form and simplify. 6/26/2018 5:52 AM 10.2 - Rational Exponents