Pre-Algebra Examples

$\frac{- 13 z^{6} v^{3} + 27 z^{6} v^{7}}{- 3 z^{3} v^{4}}$

Step 1

Factor $z^{6} v^{3}$ out of $- 13 z^{6} v^{3} + 27 z^{6} v^{7}$ .

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Step 1.1

Factor $z^{6} v^{3}$ out of $- 13 z^{6} v^{3}$ .

$\frac{z^{6} v^{3} (- 13) + 27 z^{6} v^{7}}{- 3 z^{3} v^{4}}$

Step 1.2

Factor $z^{6} v^{3}$ out of $27 z^{6} v^{7}$ .

$\frac{z^{6} v^{3} (- 13) + z^{6} v^{3} (27 v^{4})}{- 3 z^{3} v^{4}}$

Step 1.3

Factor $z^{6} v^{3}$ out of $z^{6} v^{3} (- 13) + z^{6} v^{3} (27 v^{4})$ .

$\frac{z^{6} v^{3} (- 13 + 27 v^{4})}{- 3 z^{3} v^{4}}$

Step 2

Cancel the common factor of $z^{6}$ and $z^{3}$ .

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Step 2.1

Factor $z^{3}$ out of $z^{6} v^{3} (- 13 + 27 v^{4})$ .

$\frac{z^{3} (z^{3} v^{3} (- 13 + 27 v^{4}))}{- 3 z^{3} v^{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $z^{3}$ out of $- 3 z^{3} v^{4}$ .

$\frac{z^{3} (z^{3} v^{3} (- 13 + 27 v^{4}))}{z^{3} (- 3 v^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{z^{3} (z^{3} v^{3} (- 13 + 27 v^{4}))}{z^{3} (- 3 v^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{z^{3} v^{3} (- 13 + 27 v^{4})}{- 3 v^{4}}$

Step 3

Cancel the common factor of $v^{3}$ and $v^{4}$ .

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Step 3.1

Factor $v^{3}$ out of $z^{3} v^{3} (- 13 + 27 v^{4})$ .

$\frac{v^{3} (z^{3} (- 13 + 27 v^{4}))}{- 3 v^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $v^{3}$ out of $- 3 v^{4}$ .

$\frac{v^{3} (z^{3} (- 13 + 27 v^{4}))}{v^{3} (- 3 v)}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{3} (z^{3} (- 13 + 27 v^{4}))}{v^{3} (- 3 v)}$

Step 3.2.3

Rewrite the expression.

$\frac{z^{3} (- 13 + 27 v^{4})}{- 3 v}$

Step 4

Move the negative in front of the fraction.

$- \frac{z^{3} (- 13 + 27 v^{4})}{3 v}$

Step 5

Rewrite $- 13$ as $- 1 (13)$ .

$- \frac{z^{3} (- 1 (13) + 27 v^{4})}{3 v}$

Step 6

Factor $- 1$ out of $27 v^{4}$ .

$- \frac{z^{3} (- 1 (13) - (- 27 v^{4}))}{3 v}$

Step 7

Factor $- 1$ out of $- 1 (13) - (- 27 v^{4})$ .

$- \frac{z^{3} (- 1 (13 - 27 v^{4}))}{3 v}$

Step 8

Move the negative in front of the fraction.

$- - \frac{z^{3} (13 - 27 v^{4})}{3 v}$

Step 9

Multiply $- 1$ by $- 1$ .

$1 \frac{z^{3} (13 - 27 v^{4})}{3 v}$

Step 10

Multiply $\frac{z^{3} (13 - 27 v^{4})}{3 v}$ by $1$ .

$\frac{z^{3} (13 - 27 v^{4})}{3 v}$

Step 11

Apply the distributive property.

$\frac{z^{3} \cdot 13 + z^{3} (- 27 v^{4})}{3 v}$

Step 12

Move $13$ to the left of $z^{3}$ .

$\frac{13 \cdot z^{3} + z^{3} (- 27 v^{4})}{3 v}$

Step 13

Rewrite using the commutative property of multiplication.

$\frac{13 z^{3} - 27 z^{3} v^{4}}{3 v}$

Step 14

Split the fraction $\frac{13 z^{3} - 27 z^{3} v^{4}}{3 v}$ into two fractions.

$\frac{13 z^{3}}{3 v} + \frac{- 27 z^{3} v^{4}}{3 v}$

Step 15

Cancel the common factor of $- 27$ and $3$ .

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Step 15.1

Factor $3$ out of $- 27 z^{3} v^{4}$ .

$\frac{13 z^{3}}{3 v} + \frac{3 (- 9 z^{3} v^{4})}{3 v}$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Factor $3$ out of $3 v$ .

$\frac{13 z^{3}}{3 v} + \frac{3 (- 9 z^{3} v^{4})}{3 (v)}$

Step 15.2.2

Cancel the common factor.

$\frac{13 z^{3}}{3 v} + \frac{3 (- 9 z^{3} v^{4})}{3 v}$

Step 15.2.3

Rewrite the expression.

$\frac{13 z^{3}}{3 v} + \frac{- 9 z^{3} v^{4}}{v}$

Step 16

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

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Step 16.1

Factor $v$ out of $- 9 z^{3} v^{4}$ .

$\frac{13 z^{3}}{3 v} + \frac{v (- 9 z^{3} v^{3})}{v}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

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

$\frac{13 z^{3}}{3 v} + \frac{v (- 9 z^{3} v^{3})}{v^{1}}$

Step 16.2.2

Factor $v$ out of $v^{1}$ .

$\frac{13 z^{3}}{3 v} + \frac{v (- 9 z^{3} v^{3})}{v \cdot 1}$

Step 16.2.3

Cancel the common factor.

$\frac{13 z^{3}}{3 v} + \frac{v (- 9 z^{3} v^{3})}{v \cdot 1}$

Step 16.2.4

Rewrite the expression.

$\frac{13 z^{3}}{3 v} + \frac{- 9 z^{3} v^{3}}{1}$

Step 16.2.5

Divide $- 9 z^{3} v^{3}$ by $1$ .

$\frac{13 z^{3}}{3 v} - 9 z^{3} v^{3}$