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

2. Division with the same base:
Quotient of Powers Property
Division with the same base:
Keep base the same and subtract exponents am an
= am-n
Use when you are diving power a with another power that has the SAME BASE! 55
= 5(5-3) = 52 53

3. 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

4. Dividing Powers with the Same Base
Divide. Write the quotient as one power. 7 5 3 x 10 9 1. 2.
Subtract exponents
Subtract 7
5 – 3 x
10 – 9 x 7 2
Think: x = x 1 e 10 9 9 4. 3. e 5 9 2 9
9 – 2 e
10 – 5 97 e 5

5. Dividing Powers with the Same Base
Simplify
5. 32 x4 y4z
Subtract exponents with like bases
6 x y2
9x(4-1)y(4-2) z
Simplify fully 6
1.5x3y2 z

6. 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

7. THE ZERO POWER Words Numbers Algebra
The zero power of any number except 0 equals 1.
1000 = 1
(–7)0 = 1
a0 = 1, if a  0

8. 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 .

9. Power of Quotient Property
Fraction raised to a power a b m am bm =
distribute power to each base in numerator and denominator and multiply it with existing exponent
Use when you are raising an entire fraction to a power, distribute and multiply the exponents 3 2 = =

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

11. Practice 1. 2. 3. 37 34
= 33
= 27
828 85 = = = 3 2 = =

12. Try the Challenge Problem
16x3y ∙ -2xy
-4xy x
Multiply straight across to make one fraction.
-32x4y2
4x2y3
Divide whole numbers
-8x4y2
x2y3
Subtract exponents and make sure all exponents in your answer are positive.
-8x2 y