Why do we use negative exponents in Math
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Why Do We Use Negative Exponents?

When you first see a negative exponent such as 2-2, it can appear confusing. Although you know that 2 squared is 4, what is 2 squared to the -2 power?

The answer is easier than it first appears, and will become simple to understand when you realize that a negative exponent is just a way of telling you to flip the number to become a fraction. Thus, 2-2 is a more streamlined way to tell you the real problem is 1/(22). In other words, the answer to 2-2 is 1/4.

Let’s consider another problem featuring a negative exponent, but with a twist. What would we do if we had 23/2-2?

To make it easy, let’s look at the problem as two different parts: 23 multiplied by 1/2-2. The first part, 2 to the third power, is 2 multiplied by 2 multiplied by 2, or 8. The second part featuring a negative exponent is a bit trickier.

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We already know that 2-2 is the equivalent of 1/4, but what happens when a fraction appears as the denominator of another fraction? If you recall from solving the quadratic formula, you must reverse the bases and multiply the top number with the bottom number. Therefore, we should reverse the 1/4 to 4/1, or 4. Then, we can multiply it by the top number, which is 1. In other words, 4 multiplied by 1 equals 4. That reads easy on paper, but to understand it best you can get algebra homework help.

At this point, we can now put the two parts back together again and solve 23/2-2 as such:

23/2-2 = 8/2-2 = 8 x 4 = 32.

In the world of mathematics, teachers, students, and scientists regularly rely on these types of shortcuts. Negative exponents aren’t meant to complicate matters, but to give you a different way to reorganize your problems. As you become more familiar with solving negative exponent problems, you will find that they are handy and apt in many situations.

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