Simplify 6xy^3z*3x^2yx^2

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

Step 1

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

Move $x^{2}$ .

$6 (x^{2} x) y^{3} z \cdot (3 y x^{2})$

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

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

$6 (x^{2} x^{1}) y^{3} z \cdot (3 y x^{2})$

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

$6 x^{2 + 1} y^{3} z \cdot (3 y x^{2})$

Add $2$ and $1$ .

$6 x^{3} y^{3} z \cdot (3 y x^{2})$

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$6 (x^{2} x^{3}) y^{3} z \cdot (3 y)$

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

$6 x^{2 + 3} y^{3} z \cdot (3 y)$

Add $2$ and $3$ .

$6 x^{5} y^{3} z \cdot (3 y)$

Step 3

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

Move $y$ .

$6 x^{5} (y \cdot y^{3}) z \cdot 3$

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

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

$6 x^{5} (y^{1} y^{3}) z \cdot 3$

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

$6 x^{5} y^{1 + 3} z \cdot 3$

Add $1$ and $3$ .

$6 x^{5} y^{4} z \cdot 3$

Step 4

Multiply $3$ by $6$ .

$18 x^{5} y^{4} z$