Simplify (a^4)^6(b^5)^-2

${(a^{4})}^{6} {(b^{5})}^{- 2}$

Multiply the exponents in ${(a^{4})}^{6}$ .

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

$a^{4 \cdot 6} {(b^{5})}^{- 2}$

Multiply $4$ by $6$ .

$a^{24} {(b^{5})}^{- 2}$

Multiply the exponents in ${(b^{5})}^{- 2}$ .

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

$a^{24} b^{5 \cdot - 2}$

Multiply $5$ by $- 2$ .

$a^{24} b^{- 10}$

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

$a^{24} \frac{1}{b^{10}}$

Combine $a^{24}$ and $\frac{1}{b^{10}}$ .

$\frac{a^{24}}{b^{10}}$