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

2. 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

3. 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

4. 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

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

6. 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 .

7. 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

8. Power of Quotient Property
Distribute power across the ( ). a b m am bm = 3 2 = =

9. Practice! 6 x 3 1.
= x
= x 2. 4 2m
= 24m
= 16m