Question

Which is equivalent to StartFraction x Superscript 3 Baseline over StartRoot x EndRoot EndFraction?

Answer 1

`\begin{equation*} \text{ x}^{(5)/(2)}\text{ \lparen option C\rparen} \end{equation*}`Step-by-step explanation:
`\begin{gathered} Given: \\ (x^3)/(√(x)) \end{gathered}`

We need to re-write x into one exponent:

`\begin{gathered} √(x)\text{ = x}^{(1)/(2)} \\ (x^3)/(√(x))=\text{ }\frac{x^3}{x^{(1)/(2)}} \end{gathered}`

Simplify:

`\begin{gathered} The\text{ operation between the exponent is division} \\ To\text{ combine the exponents, we will subtract the 1/2 from 3} \\ \frac{x^3}{x^{(1)/(2)}}\text{ = x}^{3-(1)/(2)} \end{gathered}`
`\begin{gathered} =\text{ x}^{(6-1)/(2)} \\ =\text{ x}^{(5)/(2)}\text{ \lparen option C\rparen} \end{gathered}`