Evaluate (3^4*b^5)^2

${(3^{4} \cdot b^{5})}^{2}$

Step 1

Raise $3$ to the power of $4$ .

${(81 \cdot b^{5})}^{2}$

Step 2

Apply the product rule to $81 b^{5}$ .

$81^{2} {(b^{5})}^{2}$

Step 3

Raise $81$ to the power of $2$ .

$6561 {(b^{5})}^{2}$

Step 4

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

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

$6561 b^{5 \cdot 2}$

Multiply $5$ by $2$ .

$6561 b^{10}$