Rational Exponents Section 7.4 1/15/2019 12:58 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 1/15/2019 12:58 AM 10.2 - Rational Exponents

THE EXPONENT 1/15/2019 12:58 AM 10.2 - Rational Exponents

NTH ROOT RULE M is the power (exponent) N is the root A is the base 1/15/2019 12:58 AM 10.2 - Rational Exponents

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? 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 10.2 - Rational Exponents

Evaluate 43/2 in radical form and simplify. EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 2 Evaluate 41/2 in radical form and simplify. 10.2 - Rational Exponents

YOUR TURN Evaluate (–27)2/3 in radical form and simplify. 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 3 Evaluate –274/3 in radical form and simplify. Use calculator to check Hint: Remember, the negative is OUTSIDE of the base 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 4 Evaluate in radical form and simplify. 1/15/2019 12:58 AM 10.2 - Rational Exponents

DROP AND SWAP NTH ROOT RULE M is the power (exponent) N is the root A is the base DROP AND SWAP 1/15/2019 12:58 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. 1/15/2019 12:58 AM 10.2 - Rational Exponents

PROPERTIES OF EXPONENTS Product of a Power: Power of a Power: Power of a Product: Negative Power Property: Quotient Power Property: 1/15/2019 12:58 AM 10.2 - Rational Exponents

If the BASES are the same, ADD the powers EXAMPLE 7 Simplify Saying goes: BASE, BASE, ADD If the BASES are the same, ADD the powers 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 8 Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents

YOUR TURN Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 9 Simplify Saying goes: POWER, POWER, MULTIPLY If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 10 Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents

YOUR TURN Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 11 Simplify Saying goes: When dividing an expression with a power, SUBTRACT the powers. 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 12 Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents

EXAMPLE 13 Simplify 1/15/2019 12:58 AM 10.2 - Rational Exponents