Simplify the Radical Expression (5^4*b^-10)^-6

${(5^{4} \cdot b^{- 10})}^{- 6}$

Raise $5$ to the power of $4$ .

${(625 \cdot b^{- 10})}^{- 6}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(625 \cdot \frac{1}{b^{10}})}^{- 6}$

Combine $625$ and $\frac{1}{b^{10}}$ .

${(\frac{625}{b^{10}})}^{- 6}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{b^{10}}{625})}^{6}$

Apply the product rule to $\frac{b^{10}}{625}$ .

$\frac{{(b^{10})}^{6}}{625^{6}}$

Multiply the exponents in ${(b^{10})}^{6}$ .

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

$\frac{b^{10 \cdot 6}}{625^{6}}$

Multiply $10$ by $6$ .

$\frac{b^{60}}{625^{6}}$

Raise $625$ to the power of $6$ .

$\frac{b^{60}}{59604644775390600}$