which is equivalent to $\frac{x^{3}}{sqrt{x}}$?\na. $x^{3/2}$\nb. $x^{2}$\nc. $x^{5/2}$\nd. $x^{7/2}$\ne…

Explanation:

Step1: Rewrite square - root as exponent

Recall that $\sqrt{x}=x^{\frac{1}{2}}$. So, $\frac{x^{3}}{\sqrt{x}}=\frac{x^{3}}{x^{\frac{1}{2}}}$.

Step2: Use exponent rule for division

The rule for dividing two terms with the same base $a^{m}\div a^{n}=a^{m - n}$. Here $a = x$, $m = 3$, and $n=\frac{1}{2}$. Then $x^{3}\div x^{\frac{1}{2}}=x^{3-\frac{1}{2}}$.

Step3: Calculate the exponent

$3-\frac{1}{2}=\frac{6 - 1}{2}=\frac{5}{2}$. So, $x^{3-\frac{1}{2}}=x^{\frac{5}{2}}$.

Answer:

C. $x^{\frac{5}{2}}$