Write in Exponential Form 1/(( square root of 3k)^5)

$\frac{1}{{(\sqrt{3 k})}^{5}}$

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

$\frac{1}{{({(3 k)}^{\frac{1}{2}})}^{5}}$

Multiply the exponents in ${({(3 k)}^{\frac{1}{2}})}^{5}$ .

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

$\frac{1}{{(3 k)}^{\frac{1}{2} \cdot 5}}$

Combine $\frac{1}{2}$ and $5$ .

$\frac{1}{{(3 k)}^{\frac{5}{2}}}$