Simplify (x^4y^3)(-5xy^3)^4

$(x^{4} y^{3}) {(- 5 x y^{3})}^{4}$

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

Apply the product rule to $- 5 x y^{3}$ .

$x^{4} y^{3} ({(- 5 x)}^{4} {(y^{3})}^{4})$

Apply the product rule to $- 5 x$ .

$x^{4} y^{3} ({(- 5)}^{4} x^{4} {(y^{3})}^{4})$

Rewrite using the commutative property of multiplication.

${(- 5)}^{4} x^{4} y^{3} (x^{4} {(y^{3})}^{4})$

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

${(- 5)}^{4} (x^{4} x^{4}) y^{3} {(y^{3})}^{4}$

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

${(- 5)}^{4} x^{4 + 4} y^{3} {(y^{3})}^{4}$

Add $4$ and $4$ .

${(- 5)}^{4} x^{8} y^{3} {(y^{3})}^{4}$

Raise $- 5$ to the power of $4$ .

$625 x^{8} y^{3} {(y^{3})}^{4}$

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

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

$625 x^{8} y^{3} y^{3 \cdot 4}$

Multiply $3$ by $4$ .

$625 x^{8} y^{3} y^{12}$

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

Move $y^{12}$ .

$625 x^{8} (y^{12} y^{3})$

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

$625 x^{8} y^{12 + 3}$

Add $12$ and $3$ .

$625 x^{8} y^{15}$