Basic Math Examples

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

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

Step 1

Multiply

3.14

$3.14$ by

{(18 u n i t s)}^{2}

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

v = \frac{4}{3} \cdot (3.14 {(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})

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

Step 3

Simplify

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

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

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Step 3.1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 3.1.1

Apply the product rule to

18 u n i t s

$18 u n i t s$ .

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

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

Step 3.1.2

Apply the product rule to

18 u n i t

$18 u n i t$ .

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

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

Step 3.1.3

Apply the product rule to

18 u n i

$18 u n i$ .

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

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

Step 3.1.4

Apply the product rule to

18 u n

$18 u n$ .

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

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

Step 3.1.5

Apply the product rule to

18 u

$18 u$ .

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

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

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

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

Step 3.2

Raise

18

$18$ to the power of

2

$2$ .

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

$i^{2}$ as

- 1

$- 1$ .

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

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

Step 3.4

Multiply

- 1

$- 1$ by

324

$324$ .

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

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

Step 3.5

Multiply

- 324

$- 324$ by

3.14

$3.14$ .

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

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

Step 3.6

Multiply

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

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

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Step 3.6.1

Combine

- 1017.36

$- 1017.36$ and

\frac{4}{3}

$\frac{4}{3}$ .

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

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

Step 3.6.2

Multiply

- 1017.36

$- 1017.36$ by

4

$4$ .

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

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

Step 3.6.3

Combine

u^{2}

$u^{2}$ and

\frac{- 4069.44}{3}

$\frac{- 4069.44}{3}$ .

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

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

Step 3.6.4

Combine

n^{2}

$n^{2}$ and

\frac{u^{2} \cdot - 4069.44}{3}

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

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

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

Step 3.6.5

Combine

t^{2}

$t^{2}$ and

\frac{n^{2} (u^{2} \cdot - 4069.44)}{3}

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

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

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

Step 3.6.6

Combine

\frac{t^{2} (n^{2} (u^{2} \cdot - 4069.44))}{3}

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

s^{2}

$s^{2}$ .

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

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

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

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

Step 3.7

Simplify the expression.

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Step 3.7.1

Move

- 4069.44

$- 4069.44$ to the left of

t^{2} n^{2} u^{2}

$t^{2} n^{2} u^{2}$ .

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

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

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}

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

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

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

Step 3.8

Factor

4069.44

$4069.44$ out of

4069.44 \cdot t^{2} n^{2} u^{2} s^{2}

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

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

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

Step 3.9

Factor

3

$3$ out of

3

$3$ .

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

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

Step 3.10

Separate fractions.

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

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

Step 3.11

Divide

4069.44

$4069.44$ by

3

$3$ .

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

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

Step 3.12

Divide

t^{2} n^{2} u^{2} s^{2}

$t^{2} n^{2} u^{2} s^{2}$ by

1

$1$ .

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

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

Step 3.13

Multiply

1356.48

$1356.48$ by

- 1

$- 1$ .

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

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

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

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