Simplify ((10xy^2)/(3z))÷((5xy)/(6z^3))

$\frac{10 x y^{2}}{3 z} \div \frac{5 x y}{6 z^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 x y^{2}}{3 z} \cdot \frac{6 z^{3}}{5 x y}$

Step 2

Combine.

$\frac{10 x y^{2} (6 z^{3})}{3 z (5 x y)}$

Step 3

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x y^{2} (6 z^{3})$ .

$\frac{5 (2 x y^{2} (6 z^{3}))}{3 z (5 x y)}$

Cancel the common factors.

Factor $5$ out of $3 z (5 x y)$ .

$\frac{5 (2 x y^{2} (6 z^{3}))}{5 (3 z (x y))}$

Cancel the common factor.

$\frac{5 (2 x y^{2} (6 z^{3}))}{5 (3 z (x y))}$

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

Factor $y$ out of $2 y^{2} (6 z^{3})$ .

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

Cancel the common factors.

Factor $y$ out of $3 z (y)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $2 y (6 z^{3})$ .

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

Cancel the common factors.

Factor $3$ out of $3 z$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

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

$\frac{z (2 y (2 z^{2}))}{z}$

Cancel the common factors.

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

$\frac{z (2 y (2 z^{2}))}{z^{1}}$

Factor $z$ out of $z^{1}$ .

$\frac{z (2 y (2 z^{2}))}{z \cdot 1}$

Cancel the common factor.

$\frac{z (2 y (2 z^{2}))}{z \cdot 1}$

Rewrite the expression.

$\frac{2 y (2 z^{2})}{1}$

Divide $2 y (2 z^{2})$ by $1$ .

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

Step 8

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 y z^{2}$

Multiply $2$ by $2$ .

$4 y z^{2}$

Simplify ((10xy^2)/(3z))÷((5xy)/(6z^3))

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