Basic Math Examples

$6 p^{4 q^{- 4}} \div 4 r p^{- 1 q^{5}}$

Step 1

Rewrite the division as a fraction.

$\frac{6 p^{4 q^{- 4}}}{4 r p^{- 1 q^{5}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $6$ and $4$ .

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Step 2.1.1

Factor $2$ out of $6 p^{4 q^{- 4}}$ .

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $4 r p^{- 1 q^{5}}$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

$\frac{3 p^{4 q^{- 4}}}{2 r p^{- 1 q^{5}}}$

Step 2.2

Cancel the common factor of $p^{4 q^{- 4}}$ and $p^{- 1 q^{5}}$ .

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Step 2.2.1

Factor $p^{- 1 q^{5}}$ out of $3 p^{4 q^{- 4}}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $p^{- 1 q^{5}}$ out of $2 r p^{- 1 q^{5}}$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3.1.2

Combine $4$ and $\frac{1}{q^{4}}$ .

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

Step 3.1.3

Multiply $q^{5}$ by $1$ .

$\frac{3 p^{\frac{4}{q^{4}} + q^{5}}}{2 r}$

Step 3.2

To write $q^{5}$ as a fraction with a common denominator, multiply by $\frac{q^{4}}{q^{4}}$ .

$\frac{3 p^{\frac{4}{q^{4}} + \frac{q^{5} q^{4}}{q^{4}}}}{2 r}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{3 p^{\frac{4 + q^{5} q^{4}}{q^{4}}}}{2 r}$

Step 3.4

Multiply $q^{5}$ by $q^{4}$ by adding the exponents.

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Step 3.4.1

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

$\frac{3 p^{\frac{4 + q^{5 + 4}}{q^{4}}}}{2 r}$

Step 3.4.2

Add $5$ and $4$ .

$\frac{3 p^{\frac{4 + q^{9}}{q^{4}}}}{2 r}$