How do you change powers with negative exponents to powers with positive exponents?

Question

I don't exacly know have to change powers with negative exponts to positive exponents. 

Answer 1

An exponent becomes negative when we are describing how many times to divide 1 (or 10⁰) by the base.  To better explain:

 

Take the example 10². This you know means multiplying by 10 twice, or 10 * 10 = 100.  

 

10² = 10*10 = 100

10¹ = 10  (which is 10²/10)

10⁰ = 1    (which is 10¹/10)

 

Notice the pattern? When you cross over to negative exponents, you just continue the pattern of dividing by the base.

 

10^-1 = 1/10  (which is 1/10 or 1/10¹)

10^-2 = 1/100 (which is 1/(10*10) or 1/10²)

10^-3 = 1/1000 (which i 1/(10*10*10) or 1/10³)

 

Once you recognize this pattern, you should be able to change any negative exponent into a positive by changing the location of the base.

 

For example, x^-2 = 1/x². I was able to get rid of the negative by moving the base to the denominator.  Similarly, I could change 1/x^-2 to just x².

 

Answer 2

In plain words, flip them over. What I mean is if you have, say, 4^-2 that's the same thing as saying 1/(4^2). Try it with a couple in your calculator to prove it to yourself.