Pre-Algebra Examples

$v^{2} \cdot (4 v) = 16 + 2 v$

Step 1

Simplify $v^{2} \cdot (4 v)$ .

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Step 1.1

Rewrite using the commutative property of multiplication.

$4 v^{2} v = 16 + 2 v$

Step 1.2

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

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Step 1.2.1

Move $v$ .

$4 (v \cdot v^{2}) = 16 + 2 v$

Step 1.2.2

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

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Step 1.2.2.1

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

$4 (v^{1} v^{2}) = 16 + 2 v$

Step 1.2.2.2

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

$4 v^{1 + 2} = 16 + 2 v$

Step 1.2.3

Add $1$ and $2$ .

$4 v^{3} = 16 + 2 v$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$v \approx 1.69225143$

Step 3