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Laws of Exponents: Powers and Products
Multiplication Rules for
Exponents
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
Multiplication Rules for
Exponents Essential
Questions
• How do I multiply powers with the
same base?
• How do I simplify a power to a
power?
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
Multiplication of Exponents
Copy the text below in to your books and then answer the
questions
a) 25 x 22 =
When multiplying:
Powers of the same
base (number) are
added.
m x an
n = am+n
In general: am
am+n
Base
number
Power
b)
c)
d)
e)
f)
g)
h)
i)
43 x 46 =
62 x 6 =
84 x 83 =
92 x 9 -2 =
2-3 x 2 =
55 x 5 –7 =
3 -2 x 3 =
8 -2 x 8 -3 =
Give your answer in
power form
Example:
55 x 56= 511
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
Multiplying powers of the same number
Answers
When multiplying:
Powers of the same base
(number) are added.
In general: am x an = am+n
Base
number
Power
a)
b)
c)
d)
e)
f)
g)
h)
i)
7
2
2 x2 =
9
4
3
6
4 x4 =
3
62 x 6 = 6
7
84 x 83 = 8
0
92 x 9 –2 = 9 =
-2 =
2
-3
2 x2 =
-2 =
5
5
–7
5 x5 =
-1
3 -2 x 3 = 3 =
1
8 -2 x 8 -3 = 8 =
5
2
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
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
4 3
3 12
3. (xy ) = x y
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
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
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
Do These Together
Simplify
4. (y3)5 =
y15
5. (m3)x = m3x
6. (x4)2 =
x8
7. (x2yx)3 = x6y3x
8. (x3y2)4 = x12y8
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
TRY THESE
Simplify
9. (y4)4 =
y16
10. (my)x = mxy
11. (x3)7 = x21
12. (x5y3)x = x5xy3x
13. (x2y5)7 = x14y35
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
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
16. (-2)3 = -8
18.
(-2x2y3)2=
4x4y6
15. -22 = -4
17. -23 = -8
19. (-3x4y2)3= -27x12y6
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
Do These Together
Simplify
20. (2y2)3 = 8y6
21. (-2m4)4 = 16m16
22. (-x2)5 = -x10
23. (-x4y6)3 = -x12y18
24. (-3x3y2)2 = 9x6y4
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Laws of Exponents: Powers and Products
TRY THESE
Simplify
25. (3y4)2 = 9y8
26. (-3m2)3 = -27m6
27. (-x3)4 = x12
28. (-x2y4)3 = -x6y12
29. (-4x2y3)2 = 16x4y6
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.