Negative Exponent

How to solve the negative exponent a-m: formula, 3 examples, and their solutions.

Formula

Formula

a-m = 1/am
(a ≠ 0)
The minus sign in the exponent means the reciprocal.
So switch the position of the power:
from the numerator to the denominator,
or from the denominator to the numerator.

Example 1

Example

Solution

x-4 = x-4/1
x-4 is in the numerator.
So move the power to the denominator.
So x-4 = 1/x4.

Example 2

Example

Solution

x-3 is in the denominator.
So move the power to the numerator.
So 1/x-3 = x3/1.
So x3 is the answer.

Example 3

Example

Change the negative exponents by moving the powers.

Solution

x-5 is in the numerator.
So move the power to the denominator.
So write x5 in the denominator.

Write y7 in the numerator.

Write x2 in the denominator.

y-1 is in the denominator.
So move the power to the numerator.
So write y (= y1) in the numerator.

So the given expression is (y7⋅y)/(x5⋅x2).

y7⋅y = y8
x5⋅x2 = x7

Product of Powers

So y8/x7 is the answer.