Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and...

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

Laws of Exponents: Powers and Products

Multiplication Rules for Exponents



Multiplication Rules for Exponents Essential

Questions

• How do I multiply powers with the same base?

• How do I simplify a power to a power?



Copy the text below in to your books and then answer the questions

When multiplying:Powers of the same base (number) are added.

In general: am x an = am+n

a) 25 x 22 =b) 43 x 46 =c) 62 x 6 =d) 84 x 83 =e) 92 x 9 -2 =f) 2-3 x 2 =g) 55 x 5 –7 =h) 3

-2 x 3 =i) 8

-2 x 8 -3 =

Give your answer in power formExample:55 x 56= 511

Base number Power



Multiplication of Exponents



Multiplying powers of the same number Answers



a) 25 x 22 =b) 43 x 46 =c) 62 x 6 =d) 84 x 83 =e) 92 x 9 –2 =f) 2-3 x 2 =g) 55 x 5 –7 =h) 3 -2 x 3 =i) 8 -2 x 8 -3 =

27

49

63

87

90 =2

-2 =5 -2 =3

-1 =8 1 =

Base numberPower



Rules and Properties

Power-of-a-Power Property

For all nonzero real numbers x and all integers m and n, (xm)n = xmn.

Example: (x2)4 = x8

(x3)x = x3x

(xy4)3 = x3y12

1.

2.

3.



Power-of-a-Product Property

For all nonzero real numbers x and y and all integers n, (xy)n = xnyn.

(xy4)3 = x3y12




Do These Together

4. (y3)5 =

Simplify

5. (m3)x =

6. (x4)2 =

7. (x2yx)3 =

8. (x3y2)4 =

y15

m3x

x8

x6y3x

x12y8



TRY THESE

9. (y4)4 =

Simplify

10. (my)x =

11. (x3)7 =

12. (x5y3)x =

13. (x2y5)7 =

y16

mxy

x21

x5xy3x

x14y35




Powers of –1

Even powers of –1 are equal to 1.

Odd powers of –1 are equal to –1.

Examples: (-2)2 = 4

(-2)3 = -8

-22 = -4

-23 = -8

(-2x2y3)2= 4x4y6 (-3x4y2)3= -27x12y6

14. 15.

16. 17.

18. 19.



Do These Together

20. (2y2)3 =

Simplify

21. (-2m4)4 =

22. (-x2)5 =

23. (-x4y6)3 =

24. (-3x3y2)2 =

8y6

16m16

-x10

-x12y18

9x6y4



TRY THESE

25. (3y4)2 =

Simplify

26. (-3m2)3 =

27. (-x3)4 =

28. (-x2y4)3 =

29. (-4x2y3)2 =

9y8

-27m6

x12

-x6y12

16x4y6

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Laws of Exponents: Powers and...

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