Write with Rational (Fractional) Exponents 1/(( square root of 3m)^3)

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

Step 1

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

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

Step 2

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

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

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

Combine $\frac{1}{2}$ and $3$ .

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