Thread: 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?

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.

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.

Great, thanks guys.

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

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