Evaluate (2a^3b^4)^4

${(2 a^{3} b^{4})}^{4}$

Step 1

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

Apply the product rule to $2 a^{3} b^{4}$ .

${(2 a^{3})}^{4} {(b^{4})}^{4}$

Apply the product rule to $2 a^{3}$ .

$2^{4} {(a^{3})}^{4} {(b^{4})}^{4}$

Step 2

Raise $2$ to the power of $4$ .

$16 {(a^{3})}^{4} {(b^{4})}^{4}$

Step 3

Multiply the exponents in ${(a^{3})}^{4}$ .

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

$16 a^{3 \cdot 4} {(b^{4})}^{4}$

Multiply $3$ by $4$ .

$16 a^{12} {(b^{4})}^{4}$

Step 4

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

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

$16 a^{12} b^{4 \cdot 4}$

Multiply $4$ by $4$ .

$16 a^{12} b^{16}$