Simplify (4d^3e^5)^7

${(4 d^{3} e^{5})}^{7}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $4 d^{3} e^{5}$ .

${(4 d^{3})}^{7} {(e^{5})}^{7}$

Apply the product rule to $4 d^{3}$ .

$4^{7} {(d^{3})}^{7} {(e^{5})}^{7}$

Raise $4$ to the power of $7$ .

$16384 {(d^{3})}^{7} {(e^{5})}^{7}$

Multiply the exponents in ${(d^{3})}^{7}$ .

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

$16384 d^{3 \cdot 7} {(e^{5})}^{7}$

Multiply $3$ by $7$ .

$16384 d^{21} {(e^{5})}^{7}$

Multiply the exponents in ${(e^{5})}^{7}$ .

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

$16384 d^{21} e^{5 \cdot 7}$

Multiply $5$ by $7$ .

$16384 d^{21} e^{35}$