Basic Math Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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Step 2.1

Move $p^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

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

Step 2.3

Add $2$ and $1$ .

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

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

Step 3

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

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Step 3.1

Factor $2$ out of $6 p^{3} q^{5} \cdot 3$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 q^{4}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{3 p^{3} q^{5} \cdot 3}{q^{4}}$

$\frac{3 p^{3} q^{5} \cdot 3}{q^{4}}$

$\frac{3 p^{3} q^{5} \cdot 3}{q^{4}}$

Step 4

Cancel the common factor of $q^{5}$ and $q^{4}$ .

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Step 4.1

Factor $q^{4}$ out of $3 p^{3} q^{5} \cdot 3$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{q^{4} (3 p^{3} q \cdot 3)}{q^{4} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{q^{4} (3 p^{3} q \cdot 3)}{q^{4} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{3 p^{3} q \cdot 3}{1}$

Step 4.2.4

Divide $3 p^{3} q \cdot 3$ by $1$ .

$3 p^{3} q \cdot 3$

$3 p^{3} q \cdot 3$

$3 p^{3} q \cdot 3$

Step 5

Multiply $3$ by $3$ .

$9 p^{3} q$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$