Question

Simplify the expression:

\[\left( \frac{ x ^{4}y ^{8} }{ x ^{6}y ^{6}} \right)^{1/2}\]

Write your answer without negative exponents.

Answer 1

I'm just gonna be honest here... I look at this expression and cringe in fear. So I'm gonna need help from the ground up.

Answer 2

you can start by dividing each exponent by 2, since everything is being raised to the power of one half

Answer 3

i.e start with
\[\frac{x^2y^4}{x^3y^3}\]

Answer 4

then subtract the exponents of the like terms

Answer 5

Okay, then we add the exponents with the same bases?

Answer 6

no, you subtract because it is a fraction (division)
if it was multiplication you would add them

Answer 7

Okay, so we get \[x ^{-1}y\]

Answer 8

since you have to write with positive exponents, subtract the smaller ones from the bigger ones

Answer 9

yeah that is right, what you wrote

Answer 10

but as i said, you want positive exponents, so i would think like this
\[\large \frac{x^2y^4}{x^3y^3}=\frac{y^{4-3}}{x^{3-2}}=\frac{y}{x}\]

Answer 11

you got the same answer

Answer 12

so its just xy?

Answer 13

no it is what i wrote

Answer 14

Okay.

Answer 15

writing with positive exponents does not mean change the minus signs to plus signs
it means use the fact that \(x^{-1}y=\frac{y}{x}\)

Answer 16

notice you could have done the subtractions first, like this
\[\left( \frac{ x ^{4}y ^{8} }{ x ^{6}y ^{6}} \right)^{1/2}=\left( \frac{ y ^{2} }{ x ^{2}} \right)^{1/2}\]
then divided the exponents by 2
either way works,whatever you think is easiest