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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