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Negative Exponents

The Importance of Negative Exponents

A negative exponent is what we get when a number raised to a power is on the wrong side of the fraction. As an example, let’s look at 152.

152 can be rewritten as 5-2, which shows the negative exponent. Another way we can think about the negative exponent is to divide by that number the amount of times that it is raised to. Since 5 is raised to the negative 2 power, we can simply divide 1 by 5 two times.

Here is what the negative exponent looks like:

5^{-2} = \frac{1}{25} = 0.04

This is how we take the number and convert it to a fraction before evaluating for an answer in decimal form.

As we may have expected, a negative exponent is the opposite of a positive exponent. They are the inverse of each other.

The best way to solve negative exponent problems is to find the positive exponent, and then take the reciprocal. We will go in depth on solving negative exponents in the section below.

How to Solve Negative Exponents

The simplest way for us to solve a negative exponent is to “flip the number to flip the sign”. All we need to remember is that moving a number across the fraction bar will flip the sign of its exponent. This applies to variables just as it does to numbers.

If a negative exponent is on the top of the fraction (which means it is the numerator), then moving it to the bottom of the fraction (making it the denominator) will cause the exponent to become positive.

Likewise, if a negative exponent is on the bottom of the fraction (meaning it is the denominator), moving it to the top of fraction (making it the numerator) will cause the exponent to become positive.

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