Dividing negative exponents?

Question

i'm stuck on a question

the only informattion they gave us is this:

x^-n

= 1/x^n

so how can i use that to help me simplify and express the answer to this question with positive exponents?

3

------------

x^-1y^-2

Answer 1

The equation they gave you is technically correct, but isn't actually the best way to think about this problem.

Here's what you need to know for negative exponents in fractions:

If you have a negative exponent on something, you can move it UP or DOWN through the fraction bar and CHANGE THE SIGN on the exponent.

So in this case, we can move x^-1 up top and change it to x^1:

3x^1

----------

y^-2

Then we can move y^-2 up top and change it to y^2:

3x^1y^2

---------

1

(We have a "1" left on bottom because we've pulled all the factors out of the bottom.)

.. = 3x^1y^2 = 3xy^2.

Answer 2

well, you know that if a negative exponent is in the numerator, the number goes into the demoninator. the variable just flips to the other one. so if the negative exponent is in the denominator, then the number goes into the numerator.

3 /  ( x^-1y^-2 )

3xy^2

I hope that helps!