Simplify (p^4q^5)^8

${(p^{4} q^{5})}^{8}$

Apply the product rule to $p^{4} q^{5}$ .

${(p^{4})}^{8} {(q^{5})}^{8}$

Multiply the exponents in ${(p^{4})}^{8}$ .

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

$p^{4 \cdot 8} {(q^{5})}^{8}$

Multiply $4$ by $8$ .

$p^{32} {(q^{5})}^{8}$

Multiply the exponents in ${(q^{5})}^{8}$ .

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

$p^{32} q^{5 \cdot 8}$

Multiply $5$ by $8$ .

$p^{32} q^{40}$

Simplify (p^4q^5)^8