EXPONENTS WITH DECIMAL AND FRACTIONAL BASES

How to Evaluate Exponents with Decimal Bases ?

Step 1 :

To evaluate exponents with decimal bases, first we have to convert the decimal bases into fractions. 

To convert the decimal base into a fraction, we have to multiply and divide the given decimal base by 10 or 100 or 1000 etc., 

Step 2 : 

After having converted the decimal base into fraction, we have to distribute the exponent to both numerator and denominator. 

How to Evaluate Exponents with Fractional Bases

To evaluate exponents with fractional bases, we have to distribute the exponent to both numerator and denominator. 

Solved Examples

Example 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

Example 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

Example 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

Example 4 :

Evaluate :

(1/2)³

Solution :

=  (1/2)³

Distribute the exponent 3 to both numerator and denominator. 

=  1³/2³

=  1/8

Example 5 :

Evaluate :

(2/5)³

Solution :

Distribute the exponent 3 to both numerator and denominator. 

=  2³/5³

=  8/125

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