Simplify (4xy^2z)(-3x^3yz^2)

$(4 x y^{2} z) (- 3 x^{3} y z^{2})$

Step 1

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

Move $x^{3}$ .

$4 (x^{3} x) y^{2} z (- 3 y z^{2})$

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

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

$4 (x^{3} x^{1}) y^{2} z (- 3 y z^{2})$

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

$4 x^{3 + 1} y^{2} z (- 3 y z^{2})$

Add $3$ and $1$ .

$4 x^{4} y^{2} z (- 3 y z^{2})$

Step 2

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

Move $y$ .

$4 x^{4} (y \cdot y^{2}) z (- 3 z^{2})$

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

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

$4 x^{4} (y^{1} y^{2}) z (- 3 z^{2})$

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

$4 x^{4} y^{1 + 2} z (- 3 z^{2})$

Add $1$ and $2$ .

$4 x^{4} y^{3} z (- 3 z^{2})$

Step 3

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

Move $z^{2}$ .

$4 x^{4} y^{3} (z^{2} z) \cdot - 3$

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

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

$4 x^{4} y^{3} (z^{2} z^{1}) \cdot - 3$

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

$4 x^{4} y^{3} z^{2 + 1} \cdot - 3$

Add $2$ and $1$ .

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

Step 4

Multiply $- 3$ by $4$ .

$- 12 x^{4} y^{3} z^{3}$