Question

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

Answer 1

$\begin{equation*} \text{ x}^{\frac{5}{2}}\text{ \lparen option C\rparen} \end{equation*}$Explanation:$\begin{gathered} Given: \\ \frac{x^3}{\sqrt{x}} \end{gathered}$

We need to re-write x into one exponent:

$\begin{gathered} \sqrt{x}\text{ = x}^{\frac{1}{2}} \\ \frac{x^3}{\sqrt{x}}=\text{ }\frac{x^3}{x^{\frac{1}{2}}} \end{gathered}$

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^{\frac{1}{2}}}\text{ = x}^{3-\frac{1}{2}} \end{gathered}$$\begin{gathered} =\text{ x}^{\frac{6-1}{2}} \\ =\text{ x}^{\frac{5}{2}}\text{ \lparen option C\rparen} \end{gathered}$