Algebra Examples

$\frac{2 x^{2} y}{6 y^{3} z} \cdot \frac{8 x^{2} y^{2} z^{2}}{7 z^{3}} \div \frac{9 x}{14 x^{2} y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x^{2} y}{6 y^{3} z} \cdot \frac{8 x^{2} y^{2} z^{2}}{7 z^{3}} \frac{14 x^{2} y}{9 x}$

Step 2

Combine.

$\frac{2 x^{2} y (8 x^{2} y^{2} z^{2})}{6 y^{3} z (7 z^{3})} \cdot \frac{14 x^{2} y}{9 x}$

Step 3

Combine.

$\frac{2 x^{2} y (8 x^{2} y^{2} z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 4

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

Tap for more steps...

Step 4.1

Move $x^{2}$ .

$\frac{2 (x^{2} x^{2}) y (8 y^{2} z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 4.2

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

$\frac{2 x^{2 + 2} y (8 y^{2} z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 4.3

Add $2$ and $2$ .

$\frac{2 x^{4} y (8 y^{2} z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 5

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

Tap for more steps...

Step 5.1

Move $y^{2}$ .

$\frac{2 x^{4} (y^{2} y) (8 z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$\frac{2 x^{4} (y^{2} y^{1}) (8 z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 5.2.2

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

$\frac{2 x^{4} y^{2 + 1} (8 z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 5.3

Add $2$ and $1$ .

$\frac{2 x^{4} y^{3} (8 z^{2}) (14 x^{2} y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 6

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $x^{2}$ .

$\frac{2 (x^{2} x^{4}) y^{3} (8 z^{2}) (14 y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 6.2

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

$\frac{2 x^{2 + 4} y^{3} (8 z^{2}) (14 y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 6.3

Add $2$ and $4$ .

$\frac{2 x^{6} y^{3} (8 z^{2}) (14 y)}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 7

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

Tap for more steps...

Step 7.1

Move $y$ .

$\frac{2 x^{6} (y \cdot y^{3}) (8 z^{2}) \cdot 14}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 7.2

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

Tap for more steps...

Step 7.2.1

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

$\frac{2 x^{6} (y^{1} y^{3}) (8 z^{2}) \cdot 14}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 7.2.2

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

$\frac{2 x^{6} y^{1 + 3} (8 z^{2}) \cdot 14}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 7.3

Add $1$ and $3$ .

$\frac{2 x^{6} y^{4} (8 z^{2}) \cdot 14}{6 y^{3} z (7 z^{3}) (9 x)}$

Step 8

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

Tap for more steps...

Step 8.1

Move $z^{3}$ .

$\frac{2 x^{6} y^{4} (8 z^{2}) \cdot 14}{6 y^{3} (z^{3} z) \cdot 7 (9 x)}$

Step 8.2

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

Tap for more steps...

Step 8.2.1

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

$\frac{2 x^{6} y^{4} (8 z^{2}) \cdot 14}{6 y^{3} (z^{3} z^{1}) \cdot 7 (9 x)}$

Step 8.2.2

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

$\frac{2 x^{6} y^{4} (8 z^{2}) \cdot 14}{6 y^{3} z^{3 + 1} \cdot 7 (9 x)}$

Step 8.3

Add $3$ and $1$ .

$\frac{2 x^{6} y^{4} (8 z^{2}) \cdot 14}{6 y^{3} z^{4} \cdot 7 (9 x)}$

Step 9

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 9.1

Factor $2$ out of $2 x^{6} y^{4} (8 z^{2}) \cdot 14$ .

$\frac{2 ((x^{6} y^{4} (8 z^{2})) \cdot 14)}{6 y^{3} z^{4} \cdot 7 (9 x)}$

Step 9.2

Cancel the common factors.

Tap for more steps...

Step 9.2.1

Factor $2$ out of $6 y^{3} z^{4} \cdot 7 (9 x)$ .

$\frac{2 ((x^{6} y^{4} (8 z^{2})) \cdot 14)}{2 (3 y^{3} z^{4} \cdot 7 (9 x))}$

Step 9.2.2

Cancel the common factor.

$\frac{2 ((x^{6} y^{4} (8 z^{2})) \cdot 14)}{2 (3 y^{3} z^{4} \cdot 7 (9 x))}$

Step 9.2.3

Rewrite the expression.

$\frac{(x^{6} y^{4} (8 z^{2})) \cdot 14}{3 y^{3} z^{4} \cdot 7 (9 x)}$

Step 10

Cancel the common factor of $x^{6}$ and $x$ .

Tap for more steps...

Step 10.1

Factor $x$ out of $(x^{6} y^{4} (8 z^{2})) \cdot 14$ .

$\frac{x ((x^{5} y^{4} (8 z^{2})) \cdot 14)}{3 y^{3} z^{4} \cdot 7 (9 x)}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $x$ out of $3 y^{3} z^{4} \cdot 7 (9 x)$ .

$\frac{x ((x^{5} y^{4} (8 z^{2})) \cdot 14)}{x (3 y^{3} z^{4} \cdot 7 \cdot (9))}$

Step 10.2.2

Cancel the common factor.

$\frac{x ((x^{5} y^{4} (8 z^{2})) \cdot 14)}{x (3 y^{3} z^{4} \cdot 7 \cdot (9))}$

Step 10.2.3

Rewrite the expression.

$\frac{(x^{5} y^{4} (8 z^{2})) \cdot 14}{3 y^{3} z^{4} \cdot 7 \cdot (9)}$

Step 11

Cancel the common factor of $y^{4}$ and $y^{3}$ .

Tap for more steps...

Step 11.1

Factor $y^{3}$ out of $(x^{5} y^{4} (8 z^{2})) \cdot 14$ .

$\frac{y^{3} (x^{5} y (8 z^{2}) \cdot 14)}{3 y^{3} z^{4} \cdot 7 \cdot (9)}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $y^{3}$ out of $3 y^{3} z^{4} \cdot 7 \cdot (9)$ .

$\frac{y^{3} (x^{5} y (8 z^{2}) \cdot 14)}{y^{3} (3 z^{4} \cdot 7 \cdot (9))}$

Step 11.2.2

Cancel the common factor.

$\frac{y^{3} (x^{5} y (8 z^{2}) \cdot 14)}{y^{3} (3 z^{4} \cdot 7 \cdot (9))}$

Step 11.2.3

Rewrite the expression.

$\frac{x^{5} y (8 z^{2}) \cdot 14}{3 z^{4} \cdot 7 \cdot (9)}$

Step 12

Cancel the common factor of $z^{2}$ and $z^{4}$ .

Tap for more steps...

Step 12.1

Factor $z^{2}$ out of $x^{5} y (8 z^{2}) \cdot 14$ .

$\frac{z^{2} (x^{5} y \cdot (8) \cdot 14)}{3 z^{4} \cdot 7 \cdot (9)}$

Step 12.2

Cancel the common factors.

Tap for more steps...

Step 12.2.1

Factor $z^{2}$ out of $3 z^{4} \cdot 7 \cdot (9)$ .

$\frac{z^{2} (x^{5} y \cdot (8) \cdot 14)}{z^{2} (3 z^{2} \cdot 7 \cdot 9)}$

Step 12.2.2

Cancel the common factor.

$\frac{z^{2} (x^{5} y \cdot (8) \cdot 14)}{z^{2} (3 z^{2} \cdot 7 \cdot 9)}$

Step 12.2.3

Rewrite the expression.

$\frac{x^{5} y \cdot (8) \cdot 14}{3 z^{2} \cdot 7 \cdot 9}$

Step 13

Cancel the common factor of $14$ and $7$ .

Tap for more steps...

Step 13.1

Factor $7$ out of $x^{5} y \cdot (8) \cdot 14$ .

$\frac{7 (x^{5} y \cdot (8) \cdot 2)}{3 z^{2} \cdot 7 \cdot 9}$

Step 13.2

Cancel the common factors.

Tap for more steps...

Step 13.2.1

Factor $7$ out of $3 z^{2} \cdot 7 \cdot 9$ .

$\frac{7 (x^{5} y \cdot (8) \cdot 2)}{7 (3 z^{2} \cdot 9)}$

Step 13.2.2

Cancel the common factor.

$\frac{7 (x^{5} y \cdot (8) \cdot 2)}{7 (3 z^{2} \cdot 9)}$

Step 13.2.3

Rewrite the expression.

$\frac{x^{5} y \cdot (8) \cdot 2}{3 z^{2} \cdot 9}$

Step 14

Simplify the expression.

Tap for more steps...

Step 14.1

Multiply $2$ by $8$ .

$\frac{x^{5} y \cdot 16}{3 z^{2} \cdot 9}$

Step 14.2

Multiply $9$ by $3$ .

$\frac{x^{5} y \cdot 16}{27 z^{2}}$

Step 14.3

Move $16$ to the left of $x^{5} y$ .

$\frac{16 x^{5} y}{27 z^{2}}$