Simplify (x^2z^3)(xy^2z)

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

Step 1

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 2

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

Move $z$ .

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

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

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

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

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

$x^{3} z^{1 + 3} y^{2}$

Add $1$ and $3$ .

$x^{3} z^{4} y^{2}$