• 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?  Reply With Quote

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.  Reply With Quote

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.  Reply With Quote

4.  Great, thanks guys.   Reply With Quote

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  Reply With Quote

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

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