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

\[\left(\frac{3^3y^4}{x^{-3}y^7}\right)^{-2}\] like that?

Answer 2

yes

Answer 3

you have a choice: you can multiply all the exponents by \(-2\) and then simplify the result, or you can simplify what is in the parentheses first and then multiply each exponent by \(-2\)

makes no difference, which would you prefer?

Answer 4

oh and i see i made a typo, it should be this:
\[\left(\frac{x^3y^4}{x^{-3}y^7}\right)^{-2}\]

Answer 5

yes

Answer 6

lets take care of what is inside the parentheses first

Answer 7

subtracting the exponents (because you are dividing) and writing with positive exponents only gives
\[\left(\frac{x^3y^4}{x^{-3}y^7}\right)^{-2}=\left(\frac{x^{3-(-3)}}{y^{7-4}}\right)^{-2}\]\[=\left(\frac{x^6}{y^3}\right)^{-2}\]

Answer 8

now the exponent outside the parentheses has a minus sign, which we can get rid of by taking the reciprocal of what is inside the parentheses, that gives
\[\left(\frac{y^3}{6^6}\right)^2\]

Answer 9

well actually it gives
\[\left(\frac{y^3}{x^6}\right)^2\]

Answer 10

now square by multiplying each exponent by 2

Answer 11

unfortunately none of your answer choices are right, so maybe there is either a typo in the question or in the answers