Question

Which of the following is a step in simplifying the expression x multiplied by y to the power of 3 over x to the power of negative 4 multiplied by y to the power of 4, the whole to the power of negative 2.?
A- x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of 8 multiplied by y to the power of negative 8.
B- x to the power of negative 2 multiplied by y, the whole over x to the power of negative 6 multiplied by y to the power of 2.
C- x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of negative 4 multiplied by y to the power of 4.
D- x to the power of negative 2 multiplied by y, the whole over x to the power of negative 4 multiplied by y to the power of 4.

Answer 1

My answer is that you can multiply many different ways to git the answers and it is really easy for you if you round your factors that you are multiply.

Answer 2

Answer:

a). x to the power of negative 2 multiplied by y to the power of negative 6, the whole over x to the power of 8 multiplied by y to the power of negative 8

Step-by-step explanation:

Given

x multiplied by y to the power of 3 over x to the power of negative 4 multiplied by y to the power of 4, the whole to the power of negative 2.

Solving we get,

$\left (\frac{xy^{3}}{x^{-4}y^{4}}\right )^{-2}$

$\left (\frac{x^{5}y^{3}}{y^{4}}\right )^{-2}$

$\left (\frac{x^{5}}{y}\right )^{-2}$

$\left (\frac{y}{x^{5}}\right )^{2}$

$\frac{y^{2}}{x^{10}}$

Now solving option A, we get

$\frac{x^{-2}y^{-6}}{x^{8}y^{-8}}$

$x^{-10}y^{2}$

$\frac{y^{2}}{x^{10}}$

Hence proved, both are equal.

Option A is the answer.