Simplify (x^3y^5)(-y^7x)

$(x^{3} y^{5}) (- y^{7} x)$

Rewrite using the commutative property of multiplication.

$- x^{3} y^{5} (y^{7} x)$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$- (x \cdot x^{3}) y^{5} y^{7}$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$- (x^{1} x^{3}) y^{5} y^{7}$

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

$- x^{1 + 3} y^{5} y^{7}$

Add $1$ and $3$ .

$- x^{4} y^{5} y^{7}$

Multiply $y^{5}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$- x^{4} (y^{7} y^{5})$

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

$- x^{4} y^{7 + 5}$

Add $7$ and $5$ .

$- x^{4} y^{12}$