1. Multiplication Rules for Exponents

2. Multiplication Rules for Exponents Essential Questions
How do I multiply powers with the same base?
How do I simplify a power to a power?

3. Multiplication of Exponents
Copy the text below in to your books and then answer the questions
25 x =
43 x =
62 x =
84 x =
92 x =
2-3 x 2 =
55 x 5 –7 =
3 -2 x =
8 -2 x 8 -3 =
When multiplying:
Powers of the same base (number) are added.
In general: am x an = am+n
When multiplying:
Powers of the same base (number) are added.
In general: am x an = am+n
Base number
Power
Give your answer in power form
Example:
55 x 56= 511

4. Multiplying powers of the same number
Answers 27 49 63 87
90 =
2 -2 =
5 -2 =
3 -1 =
8 1 =
25 x =
43 x =
62 x =
84 x =
92 x 9 –2 =
2-3 x =
55 x 5 –7 =
3 -2 x =
8 -2 x 8 -3 =
When multiplying:
Powers of the same base (number) are added.
In general: am x an = am+n
Base number
Power

5. Rules and Properties Power-of-a-Power Property
For all nonzero real numbers x and all integers m and n, (xm)n = xmn.
Example: 1.
(x2)4 = x8 2.
(x3)x = x3x
(xy4)3 = x3y12 3.

6. Power-of-a-Product Property
Rules and Properties
Power-of-a-Product Property
For all nonzero real numbers x and y and all integers n, (xy)n = xnyn.
(xy4)3 = x3y12

7. Do These Together Simplify 4. (y3)5 = y15 5. (m3)x = m3x 6. (x4)2 = x8
7. (x2yx)3 =
x6y3x
8. (x3y2)4 =
x12y8

8. TRY THESE Simplify 9. (y4)4 = y16 10. (my)x = mxy 11. (x3)7 = x21
x5xy3x
13. (x2y5)7 =
x14y35

9. Even powers of –1 are equal to 1. Odd powers of –1 are equal to –1.
Rules and Properties
Powers of –1
Even powers of –1 are equal to 1.
Odd powers of –1 are equal to –1.
Examples:
14.
(-2)2 = 4
15.
-22 = -4
16.
(-2)3 = -8
17.
-23 = -8
-27x12y6
18.
(-2x2y3)2=
4x4y6
19.
(-3x4y2)3=

10. Do These Together Simplify 20. (2y2)3 = 8y6 21. (-2m4)4 = 16m16
22. (-x2)5 =
-x10
23. (-x4y6)3 =
-x12y18
24. (-3x3y2)2 =
9x6y4

11. TRY THESE Simplify 25. (3y4)2 = 9y8 26. (-3m2)3 = -27m6 27. (-x3)4 =
28. (-x2y4)3 =
-x6y12
29. (-4x2y3)2 =
16x4y6