Question

simplify the expression
(x^3y^4 over x^-3y^7)^-2
A. y^3 over x^7
B. x^3 over y
C. y^6 over x^10
D. x^-6 over y^-5
Please help?

Answer 1

Okay. So right now your expression is \[(\frac{ x^3y^4 }{ x^{-3} y^7 })^{-3}\]

Answer 2

And lets ignore the -2 outside the parentheses right now. What can you see that is a negative? It is the x^-3 in the denominator. Do you think we can do something to it to make it positive?

Answer 3

Well whenever there is an negative in a fraction, all you have to do is switch it. If the negative is in the numerator, then you move the whole variable to the denominator. Vise versa, if the negative is in the denominator, you move the whole variable to the numerator.

Answer 4

So after you follow that, you should be able to get
\[(\frac{ x ^{3}x ^{3}y ^{4} }{ y ^{7} })^{-2}\]

Answer 5

Now whenever it is \[For example: x ^{2}x ^{4}=x ^{2+4}=x ^{6}\]

Answer 6

Therefore, it will become \[(\frac{ x ^{6}y ^{4} }{ y7 })^{-2}\]

Answer 7

Now for the y, it is the same as \[\frac{ y^4 }{ y^7 }=y ^{7-4}=y ^{3}\]

Answer 8

Therefore \[(\frac{ x^6 }{ x^7 }）^{-2}\]

And right now you have a -2 on the outside of the parentheses, to make it positive, you must put the whole parentheses under 1.

\[\frac{ 1 }{ (\frac{ x^6 }{ y^4 })^{2} }\]