Easy Algebra Step-by-Step

50 Easy Algebra Step-by-Step

Negative Integer Exponents

If x is a nonzero real number and n is a natural number, then x

x

n

n

− =^1.

A negative integer exponent on a non-

zero number tells you to obtain the recip-

rocal of the corresponding exponential

expression that has a positive exponent.

Problem Evaluate.

a. 2 −^5

b. ()−^5

c. (..^6 )−^2

d.

3

4

3

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

−

Solution

a. 2 −^5

Step 1. Write the reciprocal of the corresponding positive exponent version

of 2 −^5.

2

1

2

5

5

− =

Step 2. Evaluate 25.

2

1

2

1

22222

1

32

5

5

− ==

222222

=

b. ()−^5

Step 1. Write the reciprocal of the corresponding positive exponent version

of ()− −^5.

()− =

()−

− 5 1

5

Step 2. Evaluate ()−^5.

()− =

()−

=

−

=

−

− =−

1 1

22222 ⋅−⋅− ⋅−⋅−

1

32

1

32

5

5

P

x

x

−−nn≠−^1 n;.xxxnn≠ xxn A negative

exponent does not make a power negative.

As you can see, the negative

exponent did not make the answer

negative; 2 1

32

− (^5) ≠−.
When you evaluate ()−^5 , the answer is negative
because ()^5 is negative. The negative exponent
is not the reason ()−^5 is negative.