Question

Question 2 (1 point) \large \sqrt[4]{XY} X \large \sqrt[4]{XY} x \large \sqrt[4]{XY} x \large \sqrt[4]{XY} = a X b Y c 4XY d XY

Answer 1

The given expression simplifies to
`\(XY * x * √(XY)\)`, making the correct choice XY. Here option D is correct.

Let's simplify the given expression step by step:

`\[\sqrt[4]{XY} * X * \sqrt[4]{XY} * x * \sqrt[4]{XY} * x * \sqrt[4]{XY}\]`

Firstly, notice that
`\(\sqrt[4]{XY} * \sqrt[4]{XY} * \sqrt[4]{XY} = \sqrt[4]{(XY)^3}\)`. Now, substitute this back into the expression:

`\[X * \sqrt[4]{(XY)^3} * x * \sqrt[4]{(XY)^3} * x * \sqrt[4]{(XY)^3}\]`

Next, we can rearrange the terms to group the similar ones:

`\[(X * x * \sqrt[4]{(XY)^3}) * (x * \sqrt[4]{(XY)^3}) * \sqrt[4]{(XY)^3}\]`

Now, notice that
`\((X * x * \sqrt[4]{(XY)^3})\)` is the same as
`\(\sqrt[4]{(XY)^4}\)`. Replace this in the expression:

`\[\sqrt[4]{(XY)^4} * (x * \sqrt[4]{(XY)^3}) * \sqrt[4]{(XY)^3}\]`

Finally,
`\(\sqrt[4]{(XY)^4}\)` simplifies to XY, so the expression becomes:

`\[XY * (x * \sqrt[4]{(XY)^3}) * \sqrt[4]{(XY)^3}\]`

This can be further simplified to:

`\[XY * x * (XY)^{(3)/(4)} * (XY)^{(3)/(4)}\]`

Now, combine the exponents:

`\[XY * x * (XY)^{(3)/(2)}\]`

The equivalent expression is
`\(XY * x * √(XY)\)`. Therefore, the correct answer is D) XY.

Complete question:

Which of the following expressions is equivalent to
`\(\sqrt[4]{XY} * X * \sqrt[4]{XY} * x * \sqrt[4]{XY} * x * \sqrt[4]{XY}\)`?

A) X

B) Y

C) 4XY

D) XY