Pre-Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

Step 4

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

Tap for more steps...

Step 4.1

Move $z$ .

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $1$ and $2$ .

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

Step 5

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

Tap for more steps...

Step 5.1

Factor $x$ out of $x y^{2} z$ .

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $x$ out of $6 x^{2} y^{2} z^{3} \cdot 3$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

Tap for more steps...

Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{z}{6 x z^{3} \cdot 3}$

Step 7

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

Tap for more steps...

Step 7.1

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

$\frac{z^{1}}{6 x z^{3} \cdot 3}$

Step 7.2

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

$\frac{z \cdot 1}{6 x z^{3} \cdot 3}$

Step 7.3

Cancel the common factors.

Tap for more steps...

Step 7.3.1

Factor $z$ out of $6 x z^{3} \cdot 3$ .

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

Step 7.3.2

Cancel the common factor.

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

Step 7.3.3

Rewrite the expression.

$\frac{1}{6 x z^{2} \cdot 3}$

Step 8

Multiply $3$ by $6$ .

$\frac{1}{18 x z^{2}}$