• # Thread: negative exponents

1. ## negative exponents

 I didn't know I had a math packet to do over the summer, so now I'm rushing to get it all done before I have my first class of pre-calc and I'm really stumped with this one problem. I need to simplify this: (2^-2 + 4^-2) ^ -1 So the 2 and the 4 are both to negative exponents, then the whole thing is in parenthesis and raised to the -1 power. I tried moving the whole equation down and getting rid of the -1 exponent, like this: 1/(2^-2 + 4^-2) Then I realized that the numbers underneath would have to go up, to give me 2^2 + 4^2 = 4 + 16 = 20. BUT then I realized I might have done it all wrong, and needed to instead distribute the exponent outside the parenthesis. Which way is right, and if it's this second way, how do I do it?

2.  Originally Posted by Taffy I need to simplify this: (2^-2 + 4^-2) ^ -1 like this: 1/(2^-2 + 4^-2) Correct. Then... PHP Code: ``` 2^-2 = 1/(2^2) = 1/4  ``` and so on, which should result in 16/5 = 3.2. But really, use a calculator to check your work. As for your mistake, you can NOT simplify (2^-2 + 4^-2) into (2^2 + 4^2)^-1. You can only factor out the -1 power if 2 and 4 were multiplied, not added.

3.  Yeah, just translate what x^-2 means, which is 1/x^2. You'll get a fraction involving fractions which you can sort out using standard methods, which boil down to multiplying numerator and denominator by some number.

4.  Great, thanks guys.

5.  x^(-n) = 1/(x^n) I'll give you an example: 5^(-1) --> x is 5; n is 1; -n is -1; so x^(-n) = 5^(-1) and 1/(x^n) = 1/(5^1) 1/(5^1) = 1/5 = 0.2

6.  Always work inside parenthesis before outside. 1/(1/2^2 + 1/4^2). I got 3.2 as final answer.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•