## NEGATIVE EXPONENTS

Consider the following exponential form.

a-b

Here the base is 'a' and the exponent is '-b'.

To evaluate a-b, first we have to change the negative sign of the exponent as positive shown below. Consider the following exponential form where the base is a fraction.

(a/b)-m

Here, the negative exponent can be changed positive as shown below. From the above two examples, it is clear that if there is a negative exponent for a base, the negative exponent can be changed as positive exponent by taking the reciprocal to the base.

## Solved Problems

Problem 1 :

Evaluate :

8-2

Solution :

=  8-2

=  (1/8)2

Distribute the exponent to numerator and denominator.

=  1/ 82

=  1/64

Problem 2 :

Evaluate :

(3/2)-3

Solution :

=  (3/2)-3

=  (2/3)3

Distribute the exponent to numerator and denominator.

=  2/ 33

=  8/27

Problem 3 :

Evaluate :

(-5/4)-2

Solution :

=  (-5/4)-2

=  (-4/5)2

Since the exponent is even, the negative sign inside the parentheses will become positive.

=  (4/5)2

Distribute the exponent to numerator and denominator.

=  4/ 52

=  16/25

Problem 4 :

Evaluate :

(-7/6)-3

Solution :

=  (-6/7)-3

=  (-6/7)3

Since the exponent is odd, the negative sign inside the parentheses will remain same.

Distribute the exponent to numerator and denominator.

=  - 6/ 73

=  - 216/343

Problem 5 :

Evaluate :

(5-2⋅ (3-4)

Solution :

=  (5-2⋅ (3-4)

=  (1/5)⋅ (1/3)4

=  (1/25)  (1/81)

=  1/2025

Problem 6 :

Evaluate :

3-4/ 2-3

Solution :

=  3-4/ 2-3

=  (1/3)4/ (1/2)3

=  (1/81) / (1/8)

=  (1/81) ⋅ (8/1)

=  8/81

Problem 7 :

It is given that a-1/3  =  4/3. Find the value of a.

Solution :

a-1/3  =  4/3

a  =  (4/3)-3/1

a  =  (4/3)-3

a  =  (3/4)3

Distribute the exponent to numerator and denominator.

a  =  3/ 43

a  =  27/64

Problem 8 :

It is given that (a/b)-x  =  (b/a)3. Find the value of x.

Solution :

(a/b)-x  =  (b/a)3

(b/a)x  =  (b/a)3

x  =  3 Apart from the stuff given above, If you need any other stuff in math, please use our google custom search here.

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