1. Understanding Exponents
Base
Exponent 4 3
Power

2. Exponential Form Expanded Form Standard Form4
Exponential Form 3 1 3 3 3
Expanded Form 3 x 3 x 3 x 3 2 4 3 3
Multiply 3x3x3x3 = 81
Standard Form 81

3. How would you write this problem using exponents?
• 2 • 2 • 2 • 2 • 2 • 2 = 27
2. (-3)(-3) (-3)(-3) =
(-3)4
3. a • a • a • a • a • a • a • a = a8
4. a • m • m • a • m  • a • a =
a4 m3
5. p • 2 • r • r • r  • p • 2 =
22 p2 r3

4. Remember… An exponent does not just mean multiply by that number!
An exponent means multiply the base times itself as many times as the exponent says.

5. WATCH OUT! Any power raised to the zero power is automatically 1!
20 = 1
560 = 1
789,890,258,972,659,8720 = 1

6. Negative Exponents? A number with a negative exponent means to…
Solve the multiplication as normal
Move the answer to the denominator of a fraction under a 1.

7. For example…
4-3 =
4 x 4 x 4
16 x 4 64
_1 _ 64

8. What if there isn’t an exponent?
There’s always an exponent!
Even if there isn’t one printed, there is always an imaginary exponent of 1.
EX:
4 = 41

9. What’s the difference? ( 5 + 5)2 vs. 52 (10) 2 5x5 10x10 25 100
PAY ATTENTION TO WHERE THE EXPONENT IS & FOLLOW THE ORDER OF OPERATIONS

10. Can you solve these problems?
1. 4( 3 + 2)2 =
4(5)2
4(5•5)
4(25)
=100
• • (-3)=
-62
2x3 + 4y (x = -2 ; y = 3)
192
4. 3(a) ( a = 5) 81
-a4 (a = 2)
-16
6. (-a)4 (a = 2) 16

11. Multiplying Exponents
When the base is the same just add the exponents together
If the bases are different you can’t combine them so solve as normal
EX:
52 x 54 = 52+4 = 56 = 5x5x5x5x5x5 = 15,625
73 x 25 = 73 x 25 = 7x7x7x2x2x2x2x2 = = 375

12. Remember the imaginary exponent
44+0 = Right??
WRONG!
44 x = 45 = 4x4x4x4x4 = 1,024