How do you solve negative powers?

Answer 1

The easiest way to solve negative powers is by writing it all out.

You already know that positive powers (regular exponents) turn from something like 33 to 3 X 3 X 3 to equal 9 X 3, or 27.

Essentially, negative powers works in a very similar manner.

2-5 works out to this in expanded form: -2 X -2 X -2 X -2 X -2.

It is best to start by multiplying that expanded form in pairs. So, you group -2 X -2, and then -2 X -2, and leave the last -2 for later. -2 X -2 is a positive 4 for both results. Now, multiply both of the 4s to get 16. Now multiply that by the remaining -2 to get -32.

Tip: A shortcut method for doing this is recognizing that if the negative exponent is odd, then the answer will be multiplied just like a regular positive exponent, but the answer will be negative, and that if the negative exponent is an even number, the answer will be just like a regular positive exponent and the result will be a positive number.

Ex: 2-3 = -8 , while 3-2 = 9.