Algebra Examples

$(15 p^{5} q r^{7}) \cdot (\frac{4}{3} p^{2} q r)$

Step 1

Multiply $p^{5}$ by $p^{2}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $p^{2}$ .

$15 (p^{2} p^{5}) q r^{7} \cdot (\frac{4}{3} \cdot (q r))$

Step 1.2

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

$15 p^{2 + 5} q r^{7} \cdot (\frac{4}{3} \cdot (q r))$

Step 1.3

Add $2$ and $5$ .

$15 p^{7} q r^{7} \cdot (\frac{4}{3} \cdot (q r))$

Step 2

Multiply $q$ by $q$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $q$ .

$15 p^{7} (q \cdot q) r^{7} \cdot (\frac{4}{3} \cdot (r))$

Step 2.2

Multiply $q$ by $q$ .

$15 p^{7} q^{2} r^{7} \cdot (\frac{4}{3} \cdot (r))$

Step 3

Multiply $r^{7}$ by $r$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $r$ .

$15 p^{7} q^{2} (r \cdot r^{7}) \cdot \frac{4}{3}$

Step 3.2

Multiply $r$ by $r^{7}$ .

Tap for more steps...

Step 3.2.1

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

$15 p^{7} q^{2} (r^{1} r^{7}) \cdot \frac{4}{3}$

Step 3.2.2

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

$15 p^{7} q^{2} r^{1 + 7} \cdot \frac{4}{3}$

Step 3.3

Add $1$ and $7$ .

$15 p^{7} q^{2} r^{8} \cdot \frac{4}{3}$

Step 4

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1

Factor $3$ out of $15 p^{7} q^{2} r^{8}$ .

$3 (5 p^{7} q^{2} r^{8}) \cdot \frac{4}{3}$

Step 4.2

Cancel the common factor.

$3 (5 p^{7} q^{2} r^{8}) \cdot \frac{4}{3}$

Step 4.3

Rewrite the expression.

$5 p^{7} q^{2} r^{8} \cdot 4$

Step 5

Multiply $4$ by $5$ .

$20 p^{7} q^{2} r^{8}$