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

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

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

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

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

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

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

Multiply $3$ by $2$ .

$a^{2} \cdot (a^{6} {(b^{4})}^{2})$

Multiply $a^{2}$ by $a^{6}$ by adding the exponents.

Move $a^{6}$ .

$a^{6} a^{2} \cdot {(b^{4})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{6 + 2} \cdot {(b^{4})}^{2}$

Add $6$ and $2$ .

$a^{8} \cdot {(b^{4})}^{2}$

Multiply the exponents in ${(b^{4})}^{2}$ .

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

$a^{8} \cdot b^{4 \cdot 2}$

Multiply $4$ by $2$ .

$a^{8} \cdot b^{8}$

$a^{8} b^{8}$

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