2. Exponents Base and Power
3² = 3 · 3 = 9
n³ = n · n · n
power
Base
3²
Remember, the power tells
you how many times you are
going to multiply the base
together!

3. Exponents Base and Power
Let’s try a few!
52 = 5 · 5 = 25
(-5)2 = -5 · -5 = 25
(-2)2 = -2 · -2 = 4
(-2)3 = -2 · -2 · -2 = -8

4. Ticket to Ride …
Negative Exponents
2-2
1
2-2
1
= 2 =
2
4
4
22
1 =
=
= 4
1
1
2-2
4 = 41622 =
· 4 16
2-2
1
4-2 = 22 = 4 = 1
2-2
42
16
4

5. Negative Exponents
Let’s try a few!
-3 = 1
x
x3
1
= g4
g-4
m2
m2c-4 = 4
c

6. Product of Powers
n³ = n · n · n
n³ · n² = n · n · n · n · n
3+2
nn5 = n5

7. Product of Powers
To multiply two numbers with the same
base, add the exponents.
82 · 87 = 89
p · p5 = p6
2c · 5c4 = 10c5

8. Product of Powers
Let’s try a few!
95 · 93 = 98
r2 · r4 = r6
7k · 3k3 = 21k4

9. Quotient of Powers
To divide two numbers with1 same
-4 = the
p
base, subtract the exponents.
p4
39
÷
37 =
32
p ÷ p5 = p-4
25
22
=
1
23
p
p
=
p5 p · p · p · p · p
=
1
p · pp·4 p · p

10. Quotient of Powers
Let’s try a few!
w7 ÷ w4 = w3
d2
d9
=
x4 y 3
x6 y
1
d7
=
y2
x2

11. Power of a Power
To raise a power to a power, multiply the
exponents.
(64)5
= 620
(a-3)7 = a-21
s2 = s · s
(s2)3 = s · s · s · s · s · s
s6 = s6

12. Power of a Power
Let’s try a few!
(g7)2 = g14
(h6)-5 = h-30

13. Power of a Product
To find a power of a product, find the power of
each factor and multiply.
= a 5 b5
(5x3y)2 = 52 x6 y2
25
(ab)5

14. Power of a Product
Let’s try a few!
(hk)6
= h6k6
(4b3c5)2 = 16b6 c10

15. Power of a Quotient
To raise a quotient to a power, raise both the
numerator and denominator to the power.
a
5
d
x2
y3
7
a5
=
d5
x14
=
y21

16. Power of a Quotient
Let’s try a few!
m
8
n
k4
e9
9
m8
=
n8
k36
=
e81

17. Power of a Zero
Any nonzero number raised to the power of zero is
ALWAYS 1! It does not matter what you are
thinking it is always 1!
1,000,0000 = 1
c0 = 1
x3b0 = x3
1
1
20 · 5r4 = 5r4

18. Power of a Zero
Let’s try a few!
4,000,9980 = 1
j0 = 1
t0s5 = s5
2w3 · m0 = 2w3