Simplify (2a^2)^2(bc^2)^3

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $2$ .

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

Step 4

Apply the product rule to $b c^{2}$ .

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

Step 5

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

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

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

Multiply $2$ by $3$ .

$4 a^{4} (b^{3} c^{6})$

$4 a^{4} b^{3} c^{6}$