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

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

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 ((xy^(3))/(x^(-4)y^(4))\right )^(-2)`

`\left ((x^(5)y^(3))/(y^(4))\right )^(-2)`

`\left ((x^(5))/(y)\right )^(-2)`

`\left ((y)/(x^(5))\right )^(2)`

`(y^(2))/(x^(10))`

Now solving option A, we get

`(x^(-2)y^(-6))/(x^(8)y^(-8))`

`x^(-10)y^(2)`

`(y^(2))/(x^(10))`

Hence proved, both are equal.

Option A is the answer.