Simplify x^2y^5(-7x^5y^2)

$x^{2} y^{5} (- 7 x^{5} y^{2})$

Step 1

Rewrite using the commutative property of multiplication.

$- 7 x^{2} y^{5} (x^{5} y^{2})$

Step 2

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$- 7 (x^{5} x^{2}) y^{5} y^{2}$

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

$- 7 x^{5 + 2} y^{5} y^{2}$

Add $5$ and $2$ .

$- 7 x^{7} y^{5} y^{2}$

Step 3

Multiply $y^{5}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$- 7 x^{7} (y^{2} y^{5})$

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

$- 7 x^{7} y^{2 + 5}$

Add $2$ and $5$ .

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