Write in Exponential Form 1/(( cube root of 5)^6)

$\frac{1}{{(\sqrt[3]{5})}^{6}}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$\frac{1}{{(5^{\frac{1}{3}})}^{6}}$

Multiply the exponents in ${(5^{\frac{1}{3}})}^{6}$ .

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

$\frac{1}{5^{\frac{1}{3} \cdot 6}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5^{2}}$