negative exponents

**Taffy** · 09-05-2012 09:41 PM

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?

**reci** · 09-06-2012 08:50 PM

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.

**Xei** · 09-06-2012 09:21 PM

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.