Algebra Examples

$\frac{6 x^{7} y^{15}}{12 x^{3} y^{5}} \cdot 8 x^{4} y$

Step 1

Rewrite using the commutative property of multiplication.

$8 \frac{6 x^{7} y^{15}}{12 x^{3} y^{5}} (x^{4} y)$

Step 2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $8$ .

$4 (2) \frac{6 x^{7} y^{15}}{12 x^{3} y^{5}} (x^{4} y)$

Step 2.2

Factor $4$ out of $12 x^{3} y^{5}$ .

$4 (2) \frac{6 x^{7} y^{15}}{4 (3 x^{3} y^{5})} (x^{4} y)$

Step 2.3

Cancel the common factor.

$4 \cdot 2 \frac{6 x^{7} y^{15}}{4 (3 x^{3} y^{5})} (x^{4} y)$

Step 2.4

Rewrite the expression.

$2 \frac{6 x^{7} y^{15}}{3 x^{3} y^{5}} (x^{4} y)$

Step 3

Combine $2$ and $\frac{6 x^{7} y^{15}}{3 x^{3} y^{5}}$ .

$\frac{2 (6 x^{7} y^{15})}{3 x^{3} y^{5}} (x^{4} y)$

Step 4

Multiply $6$ by $2$ .

$\frac{12 (x^{7} y^{15})}{3 x^{3} y^{5}} (x^{4} y)$

Step 5

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

Tap for more steps...

Step 5.1

Factor $x^{3} y$ out of $3 x^{3} y^{5}$ .

$\frac{12 (x^{7} y^{15})}{x^{3} y (3 y^{4})} (x^{4} y)$

Step 5.2

Factor $x^{3} y$ out of $x^{4} y$ .

$\frac{12 (x^{7} y^{15})}{x^{3} y (3 y^{4})} (x^{3} y (x))$

Step 5.3

Cancel the common factor.

$\frac{12 (x^{7} y^{15})}{x^{3} y (3 y^{4})} (x^{3} y x)$

Step 5.4

Rewrite the expression.

$\frac{12 (x^{7} y^{15})}{3 y^{4}} x$

Step 6

Combine $\frac{12 (x^{7} y^{15})}{3 y^{4}}$ and $x$ .

$\frac{12 (x^{7} y^{15}) x}{3 y^{4}}$

Step 7

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

$\frac{12 (x^{1} x^{7} y^{15})}{3 y^{4}}$

Step 8

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

$\frac{12 (x^{1 + 7} y^{15})}{3 y^{4}}$

Step 9

Add $1$ and $7$ .

$\frac{12 (x^{8} y^{15})}{3 y^{4}}$

Step 10

Cancel the common factor of $12$ and $3$ .

Tap for more steps...

Step 10.1

Factor $3$ out of $12 (x^{8} y^{15})$ .

$\frac{3 (4 (x^{8} y^{15}))}{3 y^{4}}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $3$ out of $3 y^{4}$ .

$\frac{3 (4 (x^{8} y^{15}))}{3 (y^{4})}$

Step 10.2.2

Cancel the common factor.

$\frac{3 (4 (x^{8} y^{15}))}{3 y^{4}}$

Step 10.2.3

Rewrite the expression.

$\frac{4 (x^{8} y^{15})}{y^{4}}$

Step 11

Cancel the common factor of $y^{15}$ and $y^{4}$ .

Tap for more steps...

Step 11.1

Factor $y^{4}$ out of $4 (x^{8} y^{15})$ .

$\frac{y^{4} (4 (x^{8} y^{11}))}{y^{4}}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Multiply by $1$ .

$\frac{y^{4} (4 (x^{8} y^{11}))}{y^{4} \cdot 1}$

Step 11.2.2

Cancel the common factor.

$\frac{y^{4} (4 (x^{8} y^{11}))}{y^{4} \cdot 1}$

Step 11.2.3

Rewrite the expression.

$\frac{4 (x^{8} y^{11})}{1}$

Step 11.2.4

Divide $4 (x^{8} y^{11})$ by $1$ .

$4 (x^{8} y^{11})$

$4 x^{8} y^{11}$