EXPONENTS WITH DECIMAL AND FRACTIONAL BASES WORKSHEET
Problem 1 :
Evaluate :
(0.2)3
Problem 2 :
Evaluate :
(0.29)2
Problem 3 :
Evaluate :
(0.01)3
Problem 4 :
Evaluate :
(1/2)3
Problem 5 :
Evaluate :
(3/5)3
Detailed Answer Key
Problem 1 :
Evaluate :
(0.2)3
Solution :
Convert the decimal 0.2 into fraction.
Because there is only one digit after the decimal point, multiply and divide 0.2 by 10 to get rid of the decimal point.
(0.2)3 = [(0.2 ⋅ 10) / 10]3
= (2 / 10)3
Distribute the exponent 3 to both numerator and denominator.
= 23 / 103
= 8 / 1000
= 0.008
Problem 2 :
Evaluate :
(0.29)2
Solution :
Convert the decimal 0.29 into fraction.
Because there are two digits after the decimal point, multiply and divide 0.29 by 100 to get rid of the decimal point.
(0.29)2 = [(0.29 ⋅ 100) / 100]2
(0.29)2 = (29/100)2
Distribute the exponent 2 to both numerator and denominator.
= 292/1002
= 292/1002
= 841/10000
= 0.0841
Problem 3 :
Evaluate :
(0.01)3
Solution :
Convert the decimal 0.01 into fraction.
Because there are two digits after the decimal point, multiply and divide 0.01 by 100 to get rid of the decimal point.
(0.01)3 = [(0.01 ⋅ 100) / 100]3
= (1/100)3
Distribute the exponent 3 to both numerator and denominator.
= 13/1003
= 1/1000000
= 0.000001
Problem 4 :
Evaluate :
(1/2)3
Solution :
= (1/2)3
Distribute the exponent 3 to both numerator and denominator.
= 13/23
= 1/8
Problem 5 :
Evaluate :
(3/5)3
Solution :
Distribute the exponent 3 to both numerator and denominator.
= 33/53
= 27/125
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