Question

How do you simplify this?
(3x^-1y^-2)^-2(x^2y^5)^-1
The negative exponents out of the parenthesis throw me off

Answer 1

then multiply each exponent inside the parentheses with the exponent outside the parentheses, maybe that will make it easier

Answer 2

\[(3x^{-1}y^{-2})^{-2}(x^2y^5)^{-1}=(3^{-2}x^2y^4)(x^{-2}y^{-5})\]

Answer 3

So can i simplify this anymore? (x^2y^4/9)(1/x^2y^5)

Answer 4

yes ignore the parentheses in the first line i wrote and add the exponents
the parentheses are not necessary when you are multiplying

Answer 5

i means add the exponents for the like terms.
for example \(x^2\times x^{-2}=x^{2-2}=x^0=1\)

Answer 6

So is the answer (x^4y^9/9)
how do i know which goes in numerator/denominator

Answer 7

That's not the answer.
\[(3x^{-1}y^{-2})^{-2}(x^2y^5)^{-1}\]\[=(3^{-2}x^{(-1)\times (-2)}y^{(-2)\times (-2)})(x^{2\times (-1)}y^{5\times (-1)})\]\[=(3^{-2}x^{2}y^{4})(x^{-2}y^{-5})\]\[=3^{-2}x^{2}x^{-2}y^{4}y^{-5}\]\[=3^{-2}x^{2+(-2)}y^{4+(-5)}\]\[=...?\]

Answer 8

1/9y ??

Answer 9

yes