Simplify (-4y^3)^2*(xy^4)^3+7x^3y^18

${(- 4 y^{3})}^{2} \cdot {(x y^{4})}^{3} + 7 x^{3} y^{18}$

Simplify each term.

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

${(- 4)}^{2} {(y^{3})}^{2} \cdot {(x y^{4})}^{3} + 7 x^{3} y^{18}$

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

$16 {(y^{3})}^{2} \cdot {(x y^{4})}^{3} + 7 x^{3} y^{18}$

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

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

$16 y^{3 \cdot 2} \cdot {(x y^{4})}^{3} + 7 x^{3} y^{18}$

Multiply $3$ by $2$ .

$16 y^{6} \cdot {(x y^{4})}^{3} + 7 x^{3} y^{18}$

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

$16 y^{6} \cdot (x^{3} {(y^{4})}^{3}) + 7 x^{3} y^{18}$

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

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

$16 y^{6} \cdot (x^{3} y^{4 \cdot 3}) + 7 x^{3} y^{18}$

Multiply $4$ by $3$ .

$16 y^{6} \cdot (x^{3} y^{12}) + 7 x^{3} y^{18}$

Multiply $y^{6}$ by $y^{12}$ by adding the exponents.

Move $y^{12}$ .

$16 (y^{12} y^{6}) \cdot x^{3} + 7 x^{3} y^{18}$

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

$16 y^{12 + 6} \cdot x^{3} + 7 x^{3} y^{18}$

Add $12$ and $6$ .

$16 y^{18} \cdot x^{3} + 7 x^{3} y^{18}$

$16 y^{18} x^{3} + 7 x^{3} y^{18}$

Add $16 y^{18} x^{3}$ and $7 x^{3} y^{18}$ .

Move $y^{18}$ .

$16 x^{3} y^{18} + 7 x^{3} y^{18}$

Add $16 x^{3} y^{18}$ and $7 x^{3} y^{18}$ .

$23 x^{3} y^{18}$