Problem 1 :
Write the following powers in words and find their values.
151, (0.4)2, 43 and 74
Problem 2 :
Write the following products using an exponent.
a. 15 ⋅ 15 ⋅ 15 ⋅ 15
b. (0.5)(0.5)(0.5)
c. x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x
d. y ⋅ y ⋅ y ⋅ y ⋅ y
Problem 3 :
Evaluate the expression m5 when m = 3.
Problem 4 :
Evaluate the expression x4 when x = 0.5.
Problem 5 :
An artist uses a cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the block of ice.
Problem 1 :
Write the following powers in words and find their values.
151, (0.4)2, 43 and 74
Solution :
Power
In words
Value
151
15 to the first power
151 = 15
(0.4)2
0.4 to the second power, or 0.4 squared
(0.4)(0.4) = 0.16
43
4 to the third power, or 4 cubed
4 ⋅ 4 ⋅ 4 = 64
74
7 to the fourth power
7 ⋅ 7 ⋅ 7 ⋅ 7 = 2401
Problem 2 :
Write the following products using an exponent.
a. 15 ⋅ 15 ⋅ 15 ⋅ 15
b. (0.5)(0.5)(0.5)
c. x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x
d. y ⋅ y ⋅ y ⋅ y ⋅ y
Solution :
a. 154 |
The base 15 is used as a factor 4 times. |
b. (0.5)3 |
The base 0.5 is used as a factor 3 times. |
c. x6 |
The base x is used as a factor 6 times. |
d. y5 |
The base y is used as a factor 5 times. |
Problem 3 :
Evaluate the expression m5 when m = 3.
Solution :
= m5
Substitute 3 for m.
= (3)5
Use 3 as a factor 5 times.
= 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3
Multiply.
= 243
Problem 4 :
Evaluate the expression x4 when x = 0.5.
Solution :
= x4
Substitute 0.5 for x.
= (0.5)4
Use 0.5 as a factor 4 times.
= (0.5)(0.5)(0.5)(0.5)
Multiply.
= 0.0625
Problem 5 :
An artist uses a cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the block of ice.
Solution :
Use the formula for volume of a cube :
V = s3
Substitute 15 for s.
= 153
Use 15 as a factor 3 times.
= 15 ⋅ 15 ⋅ 15
Multiply.
= 3375
The volume of the block of ice is 3375 cubic inches.
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