Write with Rational (Fractional) Exponents ( square root of 3m)^2

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 m}$ as ${(3 m)}^{\frac{1}{2}}$ .

${({(3 m)}^{\frac{1}{2}})}^{2}$

Step 2

Multiply the exponents in ${({(3 m)}^{\frac{1}{2}})}^{2}$ .

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

${(3 m)}^{\frac{1}{2} \cdot 2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 m)}^{\frac{1}{2} \cdot 2}$

Rewrite the expression.

${(3 m)}^{1}$

Step 3

Simplify.

$3 m$