Simplify (5a^2xy^3)(b^3y^4)^3

$(5 a^{2} x y^{3}) {(b^{3} y^{4})}^{3}$

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

$5 a^{2} x y^{3} ({(b^{3})}^{3} {(y^{4})}^{3})$

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

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

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

Multiply $3$ by $3$ .

$5 a^{2} x y^{3} (b^{9} {(y^{4})}^{3})$

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

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

$5 a^{2} x y^{3} (b^{9} y^{4 \cdot 3})$

Multiply $4$ by $3$ .

$5 a^{2} x y^{3} (b^{9} y^{12})$

Multiply $y^{3}$ by $y^{12}$ by adding the exponents.

Move $y^{12}$ .

$5 a^{2} x (y^{12} y^{3}) b^{9}$

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

$5 a^{2} x y^{12 + 3} b^{9}$

Add $12$ and $3$ .

$5 a^{2} x y^{15} b^{9}$