How to Find Negative Exponents
Finding Negative Exponents
A power with a negative exponent is equal to the reciprocal of the power (1 over the power) with the exponent made positive.
Imagine we have the number 2 with an exponent of n. We put the whole power under 1 and remove the minus sign from the exponent. This is equal to ^{1}⁄_{2n}.
This is a laws of exponents.
How to Find Negative Exponents
Question
Use the law of exponents to find the power with the negative exponent below.
StepbyStep:
2
Write the power from the question on the bottom of the fraction (called the denominator).
3
Remove the minus sign from the exponent. In our example, the exponent of −2 becomes 2.
We have used the law of exponents to express the power with a negative exponent as a power with a positive exponent.
As the final step, evaluate the power with the positive exponent.
4
Evaluate the power on the bottom of the fraction. In our example, evaluate 3^{2}.
3^{2} = 3 × 3 = 9
Answer:
We have found the negative exponent.
Understanding Finding a Negative Exponent
Let us look at the rule for negative exponents:

2^{−n} and 2^{n} are powers.

The bases of the powers are 2.

The exponent of 2^{−n} is −n and the exponent of 2^{n} is n.

The fraction ^{1}⁄_{2n} is the reciprocal of 2^{n}.