Question

Use the properties of exponents to simplify the expression. (Shown in image)

Answer 1

Answer:
`(y^(6))/(x^(2))`Step-by-step explanation:

The given expression is:

`(y^{(3)/(2)}x^{-(1)/(2)})^4`

Note from the rule of indices that:

`(ab)^c=a^cb^c`

Applying this rule to the given expression, we have:

`\begin{gathered} y^{4((3)/(2))}* x^{-(1)/(2)(4)} \\ \end{gathered}`

This can be further simplified as:

`\begin{gathered} y^(2(3))* x^(-2) \\ y^6x^(-2) \end{gathered}`

Therefore, the simplified expression is:

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