Evaluate (5a^(3n))^3

${(5 a^{3 n})}^{3}$

Step 1

Apply the product rule to $5 a^{3 n}$ .

$5^{3} {(a^{3 n})}^{3}$

Step 2

Raise $5$ to the power of $3$ .

$125 {(a^{3 n})}^{3}$

Step 3

Multiply the exponents in ${(a^{3 n})}^{3}$ .

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

$125 a^{3 n \cdot 3}$

Multiply $3$ by $3$ .

$125 a^{9 n}$