Algebra Examples

$\frac{(2 p q) (3 p^{2} q^{4})}{- 6 p q^{5}}$

Step 1

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

Tap for more steps...

Step 1.1

Move $p^{2}$ .

$\frac{2 (p^{2} p) q (3 q^{4})}{- 6 p q^{5}}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{2 (p^{2} p^{1}) q (3 q^{4})}{- 6 p q^{5}}$

Step 1.2.2

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

$\frac{2 p^{2 + 1} q (3 q^{4})}{- 6 p q^{5}}$

Step 1.3

Add $2$ and $1$ .

$\frac{2 p^{3} q (3 q^{4})}{- 6 p q^{5}}$

Step 2

Multiply $q$ by $q^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $q^{4}$ .

$\frac{2 p^{3} (q^{4} q) \cdot 3}{- 6 p q^{5}}$

Step 2.2

Multiply $q^{4}$ by $q$ .

Tap for more steps...

Step 2.2.1

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

$\frac{2 p^{3} (q^{4} q^{1}) \cdot 3}{- 6 p q^{5}}$

Step 2.2.2

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

$\frac{2 p^{3} q^{4 + 1} \cdot 3}{- 6 p q^{5}}$

Step 2.3

Add $4$ and $1$ .

$\frac{2 p^{3} q^{5} \cdot 3}{- 6 p q^{5}}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $2$ out of $2 p^{3} q^{5} \cdot 3$ .

$\frac{2 (p^{3} q^{5} \cdot 3)}{- 6 p q^{5}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $- 6 p q^{5}$ .

$\frac{2 (p^{3} q^{5} \cdot 3)}{2 (- 3 p q^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (p^{3} q^{5} \cdot 3)}{2 (- 3 p q^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{p^{3} q^{5} \cdot 3}{- 3 p q^{5}}$

Step 4

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

Tap for more steps...

Step 4.1

Factor $p$ out of $p^{3} q^{5} \cdot 3$ .

$\frac{p (p^{2} q^{5} \cdot 3)}{- 3 p q^{5}}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $p$ out of $- 3 p q^{5}$ .

$\frac{p (p^{2} q^{5} \cdot 3)}{p (- 3 q^{5})}$

Step 4.2.2

Cancel the common factor.

$\frac{p (p^{2} q^{5} \cdot 3)}{p (- 3 q^{5})}$

Step 4.2.3

Rewrite the expression.

$\frac{p^{2} q^{5} \cdot 3}{- 3 q^{5}}$

Step 5

Cancel the common factor of $q^{5}$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{p^{2} q^{5} \cdot 3}{- 3 q^{5}}$

Step 5.2

Rewrite the expression.

$\frac{p^{2} \cdot 3}{- 3}$

Step 6

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

Tap for more steps...

Step 6.1

Factor $3$ out of $p^{2} \cdot 3$ .

$\frac{3 \cdot p^{2}}{- 3}$

Step 6.2

Move the negative one from the denominator of $\frac{p^{2}}{- 1}$ .

$- 1 \cdot p^{2}$

Step 7

Rewrite $- 1 \cdot p^{2}$ as $- p^{2}$ .

$- p^{2}$