Simplify (10x^3yz^2)(-2xy^5z)

$(10 x^{3} y z^{2}) (- 2 x y^{5} z)$

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

Move $x$ .

$10 (x \cdot x^{3}) y z^{2} (- 2 y^{5} z)$

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

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

$10 (x^{1} x^{3}) y z^{2} (- 2 y^{5} z)$

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

$10 x^{1 + 3} y z^{2} (- 2 y^{5} z)$

Add $1$ and $3$ .

$10 x^{4} y z^{2} (- 2 y^{5} z)$

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

Move $y^{5}$ .

$10 x^{4} (y^{5} y) z^{2} (- 2 z)$

Multiply $y^{5}$ by $y$ .

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

$10 x^{4} (y^{5} y^{1}) z^{2} (- 2 z)$

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

$10 x^{4} y^{5 + 1} z^{2} (- 2 z)$

Add $5$ and $1$ .

$10 x^{4} y^{6} z^{2} (- 2 z)$

Multiply $z^{2}$ by $z$ by adding the exponents.

Move $z$ .

$10 x^{4} y^{6} (z \cdot z^{2}) \cdot - 2$

Multiply $z$ by $z^{2}$ .

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

$10 x^{4} y^{6} (z^{1} z^{2}) \cdot - 2$

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

$10 x^{4} y^{6} z^{1 + 2} \cdot - 2$

Add $1$ and $2$ .

$10 x^{4} y^{6} z^{3} \cdot - 2$

Multiply $- 2$ by $10$ .

$- 20 x^{4} y^{6} z^{3}$