Name Class Date Practice
Form G
Multiplying Powers With the Same Base
Rewrite each expression using each base only once.
# 43 48
4.10-4 # 104 # 102 102
# 26 # 22 212
5. 79 # 73 # 7-10 72
1.45
# 5-2 # 5-1 53
6. 92 # 9-8 # 96 90
2. 24
Simplify each expression.
8. -4k -3
7.z 8z 5 z 13
3. 56
# 6k4
9. (-5b3)(-3b6)
15b9
−24k
10. (13x -8)(3x 10)
39 x 2
13. mn2
m4
11. (-2h5)(4h-3)
12. -8n
−88n10
−8h2
# m2n-4 # mn-1
14. (6a3b-2)(-4ab-8)
−
n3
# 11n9
15. (12mn)(-m3n-2p5)(2m)
24a4
−
b10
24m5p5
n
Write each answer in scientific notation.
16. The population of a country in 1950 was 6.2 * 107. The population in 2030 is
projected to be 3 * 102 times the 1950 population. If the projection is correct,
what will the population of the country be in 2030? 1.86 × 1010
17. The area of land that Rhode Island covers is approximately 1.5 * 103 square miles.
The area of land that Alaska covers is a little more than 4.3 * 102 times the land
area of Rhode Island. What is the approximate area of Alaska in square miles?
6.45 × 105 mi2
Simplify each expression.
1
1
18. 164 2
4
□
23. 252 125
# 6r b # a7q # 6r b 25. a3h # 2k b # a2k # 3h b 26. a8p # 5m b # a8p # 5m b
3
5
5
1
3
5
2
1
5
# 94 = 9□
# z-5 = z3
3
4
15
4
3
2
5
4
□
2
28. 5
8
31. m3
1
# 53 = 52 −1
# m # m□ = m2
1
6
1
6
1
2
5
9
1
4
5
6
4
64p12 25m 3
9h 4 4k 4
Complete each equation.
30. z
3
22. 643 256
49q 3 36r 5
27. 9-2
20. 243 5 3
4
2
21. 83 4
24. a7q3
1
19. 1253 5
# 2□ = 2-2 −10
□
32. d 7 # d -13 # d -9 = d
29. 28
3
2
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−15
Name Class Date Practice (continued)
Form G
Multiplying Powers With the Same Base
Find the area of each figure.
33.
3x 2 + 2x
34.
3n 2
4x 2
6n + 5
12x 4 + 8x 3
35.
18n3 + 15n2
36.
4
3z
HSM11A1TR_0703_T002
HSM11A1TR_0703_T001
5b
2b 2 – 4
5b3 − 10b
9z 8
HSM11A1TR_0703_T003
Simplify each expression. Write each answer in scientific notation.
37. (7 * 1017)(8 * 10-28)
5.6 × 10−10
38. (4 * 10-11)(0.8
* 107)
39. (0.9 * 1015)(0.1 * 10-6)
HSM11A1TR_0703_T004
3.2 × 10−4
40. (0.8 * 105)(0.6 * 10-17)
4.8 × 10−13
41. (0.5 * 103)(0.6 * 100)
3.0 × 102
9.0 × 107
42. (0.2 * 1011)(0.4 * 10-14)
8.0 × 10−5
43. The diameter of the moon is approximately 3.5 * 103 kilometers.
a. The diameter of Earth is approximately 3.7 times the diameter of the moon.
Determine the diameter of Earth. Write your answer in scientific notation. 1.295 × 104 km
b.
The distance from the center of Earth to the center of the moon is
approximately 30 times the diameter of Earth. Determine the distance
from the center of Earth to the center of the moon. Write your answer in
scientific notation. 3.885 × 105 km
Simplify each expression.
#
#
44. -8 1 3 n5
n
n
1
45. 4 1 -9 x 5
x
x
47. -2x2a -3x 2 + 5 b 5
6x 2 − 10x 2
48. 4x
# 4x+1 # 4
42x+2
10
5
46. 7k 4(-2k 6 - k) −14k − 7k
49. (n + 2)5(n + 2)-3
n2 + 4n + 4
50. Writing Explain what moving the decimal point 4 places to the right or to the
left does to the value of a number. In scientific notation, what power of 10 would
you multiply by to move the decimal point 4 places to the right or to the left?
Moving the decimal point 4 places to the right multiplies a number by 10,000. In
scientific notation, multiplying by 104 would be the same. Moving the decimal point
4 places to the left divides a number by 10,000. In scientific notation, you would
multiply by 10−4 .
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