Help with negative exponets

[samburger_happymeal]

Hey guys! Having some difficulty with this problem. Ive worked it several times but cant get the answer right. Heres the problem:

a^-2+b^-1/a^-1(b)

The answer is:

b+a^2/ab^2

Im pretty stuck and if anyone can possibly explain it to me that would be awesome!
Thanks everyone
Samburger

 

[tkhunny]

Sadly, I cannot translate what you have written. Please add parentheses as necessary to clarify.

Hint: "(a + b)/2" is NOT the same as "a + b / 2"

 

[samburger_happymeal]

Sorry! Does this help?

Problem: a(^-2)+ b(^-1) / (a^-1)b
answer: b + a^2 / ab^2

 

[tkhunny]

Actually, that was worse. Please try to remember the proper use of parentheses. It never would be to separate an exponent from tis base.

I'll just give it a try...

\(\displaystyle \frac{a^{-2}+b^{-1}}{a^{-1}\cdot b}\)

There are a few ways to go about it.

First, let's agree that 'a' is NOT zero and 'b' is NOT zero.
Second, a/a = 1 and b/b = 1.

Multiple the expression by 'a/a'

\(\displaystyle \frac{a^{-1}+a\cdot b^{-1}}{b}\)

Do it again.

\(\displaystyle \frac{1+a^{2}\cdot b^{-1}}{a\cdot b}\)

Multiple the expression by 'b/b'

\(\displaystyle \frac{b+a^{2}}{a\cdot b^{2}}\)

Hmmm.... It appears I guessed correctly.