# EXPONENTS WITH DECIMAL AND FRACTIONAL BASES WORKSHEET

Exponents with Decimal and Fractional Bases Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on evaluating exponents with decimal and fractional bases.

Before look at the worksheet, if you would like to know, how to evaluate exponents with decimal and fractional bases,

Problem 1 :

Evaluate :

(2/5)3

Problem 2 :

Evaluate :

(0.2)3

Problem 3 :

Evaluate :

(0.29)2

Problem 4 :

Evaluate :

(0.01)3

Problem 5 :

Evaluate :

(5/2)3

## Exponents with Decimal and Fractional Bases Worksheet - Solutions

Problem 1 :

Evaluate :

(2/5)3

Solution :

Distribute the exponent 3 to both numerator and denominator.

(2/5)3  =  23/33

(2/5)3  =  8/27

Problem 2 :

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

(0.2)3  =  (2 / 10)3

Distribute the exponent 3 to both numerator and denominator.

(0.2)3  =  23 / 103

(0.2)3  =  8 / 1000

(0.2)3  =  0.008

Problem 3 :

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.

(0.29)2  =  292/1002

(0.29)2  =  292/1002

(0.29)2  =  841/10000

(0.29)2  =  0.0841

Problem 4 :

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

(0.01)3  =  (1/100)3

Distribute the exponent 3 to both numerator and denominator.

(0.01)3  =  13/1003

(0.01)3  =  1/1000000

(0.01)3  =  0.000001

Problem 5 :

Evaluate :

(5/2)3

Solution :

Distribute the exponent 3 to both numerator and denominator.

(5/2)3  =  53/23

(5/2)3  =  125/8

After having gone through the stuff given above, we hope that the students would have understood, how to write a fraction in its lowest term using divisibility rules.

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