Basic Math Examples

${(2 p^{5} q^{6})}^{3} \div 4 p^{2} q^{8}$

Step 1

Rewrite the division as a fraction.

$\frac{{(2 p^{5} q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 p^{5} q^{6}$ .

$\frac{{(2 p^{5})}^{3} {(q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2.2

Apply the product rule to $2 p^{5}$ .

$\frac{2^{3} {(p^{5})}^{3} {(q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2.3

Raise $2$ to the power of $3$ .

$\frac{8 {(p^{5})}^{3} {(q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2.4

Multiply the exponents in ${(p^{5})}^{3}$ .

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Step 2.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{8 p^{5 \cdot 3} {(q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2.4.2

Multiply $5$ by $3$ .

$\frac{8 p^{15} {(q^{6})}^{3}}{4 p^{2} q^{8}}$

Step 2.5

Multiply the exponents in ${(q^{6})}^{3}$ .

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Step 2.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{8 p^{15} q^{6 \cdot 3}}{4 p^{2} q^{8}}$

Step 2.5.2

Multiply $6$ by $3$ .

$\frac{8 p^{15} q^{18}}{4 p^{2} q^{8}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $8$ and $4$ .

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Step 3.1.1

Factor $4$ out of $8 p^{15} q^{18}$ .

$\frac{4 (2 p^{15} q^{18})}{4 p^{2} q^{8}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $4 p^{2} q^{8}$ .

$\frac{4 (2 p^{15} q^{18})}{4 (p^{2} q^{8})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 (2 p^{15} q^{18})}{4 (p^{2} q^{8})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{2 p^{15} q^{18}}{p^{2} q^{8}}$

Step 3.2

Cancel the common factor of $p^{15}$ and $p^{2}$ .

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Step 3.2.1

Factor $p^{2}$ out of $2 p^{15} q^{18}$ .

$\frac{p^{2} (2 p^{13} q^{18})}{p^{2} q^{8}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $p^{2}$ out of $p^{2} q^{8}$ .

$\frac{p^{2} (2 p^{13} q^{18})}{p^{2} (q^{8})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{p^{2} (2 p^{13} q^{18})}{p^{2} q^{8}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{2 p^{13} q^{18}}{q^{8}}$

Step 3.3

Cancel the common factor of $q^{18}$ and $q^{8}$ .

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Step 3.3.1

Factor $q^{8}$ out of $2 p^{13} q^{18}$ .

$\frac{q^{8} (2 p^{13} q^{10})}{q^{8}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Multiply by $1$ .

$\frac{q^{8} (2 p^{13} q^{10})}{q^{8} \cdot 1}$

Step 3.3.2.2

Cancel the common factor.

$\frac{q^{8} (2 p^{13} q^{10})}{q^{8} \cdot 1}$

Step 3.3.2.3

Rewrite the expression.

$\frac{2 p^{13} q^{10}}{1}$

Step 3.3.2.4

Divide $2 p^{13} q^{10}$ by $1$ .

$2 p^{13} q^{10}$