Basic Math Examples

$v = \frac{4}{3} \cdot ((3.14) {(18 u n i t s)}^{2})$

Step 1

Multiply $3.14$ by ${(18 u n i t s)}^{2}$ .

$v = \frac{4}{3} \cdot (3.14 {(18 u n i t s)}^{2})$

Step 2

Remove parentheses.

$v = \frac{4}{3} \cdot (3.14 {(18 u n i t s)}^{2})$

Step 3

Simplify $\frac{4}{3} \cdot (3.14 {(18 u n i t s)}^{2})$ .

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Step 3.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1.1

Apply the product rule to $18 u n i t s$ .

$v = \frac{4}{3} \cdot (3.14 ({(18 u n i t)}^{2} s^{2}))$

Step 3.1.2

Apply the product rule to $18 u n i t$ .

$v = \frac{4}{3} \cdot (3.14 ({(18 u n i)}^{2} t^{2} s^{2}))$

Step 3.1.3

Apply the product rule to $18 u n i$ .

$v = \frac{4}{3} \cdot (3.14 ({(18 u n)}^{2} i^{2} t^{2} s^{2}))$

Step 3.1.4

Apply the product rule to $18 u n$ .

$v = \frac{4}{3} \cdot (3.14 ({(18 u)}^{2} n^{2} i^{2} t^{2} s^{2}))$

Step 3.1.5

Apply the product rule to $18 u$ .

$v = \frac{4}{3} \cdot (3.14 (18^{2} u^{2} n^{2} i^{2} t^{2} s^{2}))$

Step 3.2

Raise $18$ to the power of $2$ .

$v = \frac{4}{3} \cdot (3.14 (324 u^{2} n^{2} i^{2} t^{2} s^{2}))$

Step 3.3

Rewrite $i^{2}$ as $- 1$ .

$v = \frac{4}{3} \cdot (3.14 (324 u^{2} n^{2} \cdot - 1 t^{2} s^{2}))$

Step 3.4

Multiply $- 1$ by $324$ .

$v = \frac{4}{3} \cdot (3.14 (- 324 u^{2} n^{2} t^{2} s^{2}))$

Step 3.5

Multiply $- 324$ by $3.14$ .

$v = \frac{4}{3} \cdot (- 1017.36 (u^{2} n^{2} t^{2} s^{2}))$

Step 3.6

Multiply $\frac{4}{3} (- 1017.36 u^{2} n^{2} t^{2} s^{2})$ .

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Step 3.6.1

Combine $- 1017.36$ and $\frac{4}{3}$ .

$v = \frac{- 1017.36 \cdot 4}{3} (u^{2} n^{2} t^{2} s^{2})$

Step 3.6.2

Multiply $- 1017.36$ by $4$ .

$v = \frac{- 4069.44}{3} (u^{2} n^{2} t^{2} s^{2})$

Step 3.6.3

Combine $u^{2}$ and $\frac{- 4069.44}{3}$ .

$v = \frac{u^{2} \cdot - 4069.44}{3} (n^{2} t^{2} s^{2})$

Step 3.6.4

Combine $n^{2}$ and $\frac{u^{2} \cdot - 4069.44}{3}$ .

$v = \frac{n^{2} (u^{2} \cdot - 4069.44)}{3} (t^{2} s^{2})$

Step 3.6.5

Combine $t^{2}$ and $\frac{n^{2} (u^{2} \cdot - 4069.44)}{3}$ .

$v = \frac{t^{2} (n^{2} (u^{2} \cdot - 4069.44))}{3} s^{2}$

Step 3.6.6

Combine $\frac{t^{2} (n^{2} (u^{2} \cdot - 4069.44))}{3}$ and $s^{2}$ .

$v = \frac{t^{2} (n^{2} (u^{2} \cdot - 4069.44)) s^{2}}{3}$

Step 3.7

Simplify the expression.

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Step 3.7.1

Move $- 4069.44$ to the left of $t^{2} n^{2} u^{2}$ .

$v = \frac{- 4069.44 \cdot (t^{2} n^{2} u^{2}) s^{2}}{3}$

Step 3.7.2

Move the negative in front of the fraction.

$v = - \frac{4069.44 \cdot t^{2} n^{2} u^{2} s^{2}}{3}$

Step 3.8

Factor $4069.44$ out of $4069.44 \cdot t^{2} n^{2} u^{2} s^{2}$ .

$v = - \frac{4069.44 (t^{2} n^{2} u^{2} s^{2})}{3}$

Step 3.9

Factor $3$ out of $3$ .

$v = - \frac{4069.44 (t^{2} n^{2} u^{2} s^{2})}{3 (1)}$

Step 3.10

Separate fractions.

$v = - (\frac{4069.44}{3} \cdot \frac{t^{2} n^{2} u^{2} s^{2}}{1})$

Step 3.11

Divide $4069.44$ by $3$ .

$v = - (1356.48 \frac{t^{2} n^{2} u^{2} s^{2}}{1})$

Step 3.12

Divide $t^{2} n^{2} u^{2} s^{2}$ by $1$ .

$v = - (1356.48 (t^{2} n^{2} u^{2} s^{2}))$

Step 3.13

Multiply $1356.48$ by $- 1$ .

$v = - 1356.48 t^{2} n^{2} u^{2} s^{2}$