Basic Math Examples

$(8 v^{3} + 81 v^{2} \cdot (15 v)) \div 27 v$

Step 1

Rewrite the division as a fraction.

$\frac{8 v^{3} + 81 v^{2} \cdot (15 v)}{27 v}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $v^{2}$ out of $8 v^{3} + 81 v^{2} \cdot (15 v)$ .

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Step 2.1.1

Factor $v^{2}$ out of $8 v^{3}$ .

$\frac{v^{2} (8 v) + 81 v^{2} \cdot (15 v)}{27 v}$

Step 2.1.2

Factor $v^{2}$ out of $81 v^{2} \cdot (15 v)$ .

$\frac{v^{2} (8 v) + v^{2} (81 \cdot (15 v))}{27 v}$

Step 2.1.3

Factor $v^{2}$ out of $v^{2} (8 v) + v^{2} (81 \cdot (15 v))$ .

$\frac{v^{2} (8 v + 81 \cdot (15 v))}{27 v}$

Step 2.2

Factor $v$ out of $8 v + 81 \cdot 15 v$ .

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Step 2.2.1

Factor $v$ out of $8 v$ .

$\frac{v^{2} (v \cdot 8 + 81 \cdot 15 v)}{27 v}$

Step 2.2.2

Factor $v$ out of $81 \cdot 15 v$ .

$\frac{v^{2} (v \cdot 8 + v (81 \cdot 15))}{27 v}$

Step 2.2.3

Factor $v$ out of $v \cdot 8 + v (81 \cdot 15)$ .

$\frac{v^{2} (v (8 + 81 \cdot 15))}{27 v}$

Step 2.3

Multiply $81$ by $15$ .

$\frac{v^{2} (v (8 + 1215))}{27 v}$

Step 2.4

Add $8$ and $1215$ .

$\frac{v^{2} v \cdot 1223}{27 v}$

Step 2.5

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

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Step 2.5.1

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

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Step 2.5.1.1

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

$\frac{v^{2} v^{1} \cdot 1223}{27 v}$

Step 2.5.1.2

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

$\frac{v^{2 + 1} \cdot 1223}{27 v}$

Step 2.5.2

Add $2$ and $1$ .

$\frac{v^{3} \cdot 1223}{27 v}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Factor $v$ out of $v^{3} \cdot 1223$ .

$\frac{v (v^{2} \cdot 1223)}{27 v}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $v$ out of $27 v$ .

$\frac{v (v^{2} \cdot 1223)}{v \cdot 27}$

Step 3.1.2.2

Cancel the common factor.

$\frac{v (v^{2} \cdot 1223)}{v \cdot 27}$

Step 3.1.2.3

Rewrite the expression.

$\frac{v^{2} \cdot 1223}{27}$

Step 3.2

Move $1223$ to the left of $v^{2}$ .

$\frac{1223 v^{2}}{27}$