Write in Exponential Form ( square root of x^3)^2

${(\sqrt{x^{3}})}^{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{3}}$ as $x^{\frac{3}{2}}$ .

${(x^{\frac{3}{2}})}^{2}$

Step 2

Multiply the exponents in ${(x^{\frac{3}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{3}{2} \cdot 2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{3}{2} \cdot 2}$

Rewrite the expression.

$x^{3}$