Divide ((81xz^3)/(36y))÷((27x^2z^2)/(12xy))

$\frac{81 x z^{3}}{36 y} \div \frac{27 x^{2} z^{2}}{12 x y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{81 x z^{3}}{36 y} \cdot \frac{12 x y}{27 x^{2} z^{2}}$

Step 2

Combine.

$\frac{81 x z^{3} (12 x y)}{36 y (27 x^{2} z^{2})}$

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{81 (x \cdot x) z^{3} (12 y)}{36 y (27 x^{2} z^{2})}$

Multiply $x$ by $x$ .

$\frac{81 x^{2} z^{3} (12 y)}{36 y (27 x^{2} z^{2})}$

Step 4

Cancel the common factor of $81$ and $36$ .

Factor $9$ out of $81 x^{2} z^{3} (12 y)$ .

$\frac{9 (9 x^{2} z^{3} (12 y))}{36 y (27 x^{2} z^{2})}$

Cancel the common factors.

Factor $9$ out of $36 y (27 x^{2} z^{2})$ .

$\frac{9 (9 x^{2} z^{3} (12 y))}{9 (4 y (27 x^{2} z^{2}))}$

Cancel the common factor.

$\frac{9 (9 x^{2} z^{3} (12 y))}{9 (4 y (27 x^{2} z^{2}))}$

Rewrite the expression.

$\frac{9 x^{2} z^{3} (12 y)}{4 y (27 x^{2} z^{2})}$

Step 5

Cancel the common factor of $9$ and $27$ .

Factor $9$ out of $9 x^{2} z^{3} (12 y)$ .

$\frac{9 (x^{2} z^{3} (12 y))}{4 y (27 x^{2} z^{2})}$

Cancel the common factors.

Factor $9$ out of $4 y (27 x^{2} z^{2})$ .

$\frac{9 (x^{2} z^{3} (12 y))}{9 (4 y (3 x^{2} z^{2}))}$

Cancel the common factor.

$\frac{9 (x^{2} z^{3} (12 y))}{9 (4 y (3 x^{2} z^{2}))}$

Rewrite the expression.

$\frac{x^{2} z^{3} (12 y)}{4 y (3 x^{2} z^{2})}$

Step 6

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} z^{3} (12 y)}{4 y (3 x^{2} z^{2})}$

Rewrite the expression.

$\frac{z^{3} (12 y)}{4 y (3 z^{2})}$

Step 7

Cancel the common factor of $z^{3}$ and $z^{2}$ .

Factor $z^{2}$ out of $z^{3} (12 y)$ .

$\frac{z^{2} (z (12 y))}{4 y (3 z^{2})}$

Cancel the common factors.

Factor $z^{2}$ out of $4 y (3 z^{2})$ .

$\frac{z^{2} (z (12 y))}{z^{2} (4 y \cdot (3))}$

Cancel the common factor.

$\frac{z^{2} (z (12 y))}{z^{2} (4 y \cdot (3))}$

Rewrite the expression.

$\frac{z (12 y)}{4 y \cdot (3)}$

Step 8

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $z (12 y)$ .

$\frac{4 (z (3 y))}{4 y \cdot (3)}$

Cancel the common factors.

Factor $4$ out of $4 y \cdot (3)$ .

$\frac{4 (z (3 y))}{4 (y \cdot (3))}$

Cancel the common factor.

$\frac{4 (z (3 y))}{4 (y \cdot (3))}$

Rewrite the expression.

$\frac{z (3 y)}{y \cdot (3)}$

Step 9

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{z (3 y)}{y \cdot 3}$

Rewrite the expression.

$\frac{z (y)}{y}$

Step 10

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{z y}{y}$

Divide $z$ by $1$ .

$z$

Divide ((81xz^3)/(36y))÷((27x^2z^2)/(12xy))

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