Exponent rules

Sometimes we are give a problem that includes multiple negative exponents. Methodically simplifying the problem in a step by step approach helps avoid mistakes. Take the following problem:

 

One option is to take the y^-3 and put it as the denominator. By doing this you can change it to a positive exponent. Now we have ((2x^4)/(y^3))^-1 (see photo below for easy to read equation). Now, let’s take the reciprocal of everything inside parentheses so that the exponent of -1 becomes 1.

And as you can see in the bottom half of the above photo, you can also begin by taking the reciprocal of the given fraction. Now that you have 1/(2x^4y^-3), you can move the y^-3 to the numerator to make it a positive exponent.  This gives you the final answer which is the same as the first method given above.