Properties of Exponents – Part 2 Division and Zero Powers Learn zero exponents and division properties of exponents.

DIVIDING POWERS WITH THE SAME BASE Notice what occurs when you divide powers with the same base. 5 53 = 5  5  5 5  5  5  5  5 = 5 • 5 = 52 DIVIDING POWERS WITH THE SAME BASE Words Numbers Algebra To divide powers with the same base, keep the base and subtract the exponents. 6 5 9 – 4 9 4 = b m – n m n

Dividing Powers with the Same Base Divide. Write the quotient as one power. 7 5 3 A. 7 5 – 3 Subtract exponents. 7 2 x 10 9 B. x 10 – 9 Subtract exponents. x Think: x = x 1

A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e Try This: Divide. Write the quotient as one power. 9 9 A. 9 2 9 9 – 2 Subtract exponents. 97 e 10 B. e 5 e 10 – 5 Subtract exponents. e 5

This result can be confirmed by writing out the factors. When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent. 1 = 4 2 42 – 2 = 40 = 1 = This result can be confirmed by writing out the factors. = (4 • 4) = 1 1 4 2

0 does not exist because 00 represents a quotient of the form But the denominator of this quotient is 0, which is impossible, since you cannot divide by 0! It is undefined! Helpful Hint 0n .

THE ZERO POWER Words Numbers Algebra The zero power of any number except 0 equals 1. 1000 = 1 (–7)0 = 1 a = 1, if a  0

Power of Quotient Property Distribute power across the ( ). a b m am bm = 3 2 = 22 32 = 4 9

Practice! 6 x 3 1. = x3 63 = x3 216 2. 4 2m = 24m4 44 = 16m4 256