Simplify (4a^2b^7)^3

${(4 a^{2} b^{7})}^{3}$

Step 1

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

Apply the product rule to $4 a^{2} b^{7}$ .

${(4 a^{2})}^{3} {(b^{7})}^{3}$

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

$4^{3} {(a^{2})}^{3} {(b^{7})}^{3}$

Step 2

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

$64 {(a^{2})}^{3} {(b^{7})}^{3}$

Step 3

Multiply the exponents in ${(a^{2})}^{3}$ .

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

$64 a^{2 \cdot 3} {(b^{7})}^{3}$

Multiply $2$ by $3$ .

$64 a^{6} {(b^{7})}^{3}$

Step 4

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

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

$64 a^{6} b^{7 \cdot 3}$

Multiply $7$ by $3$ .

$64 a^{6} b^{21}$