Basic Math Examples

$v = \frac{4}{3} \cdot ((3.14) {(6 u n i t s)}^{3})$

Step 1

Rewrite the equation as $\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3}) = v$ .

$\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3}) = v$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{4}{3} \cdot 3.14}$ .

$\frac{1}{\frac{4}{3} \cdot 3.14} (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{1}{\frac{4}{3} \cdot 3.14} (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3}))$ .

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Step 3.1.1.1

Combine $\frac{4}{3}$ and $3.14$ .

$\frac{1}{\frac{4 \cdot 3.14}{3}} (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.2

Simplify the expression.

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Step 3.1.1.2.1

Multiply $4$ by $3.14$ .

$\frac{1}{\frac{12.56}{3}} (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.2.2

Divide $12.56$ by $3$ .

$\frac{1}{4.18\overline{6}} (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.2.3

Divide $1$ by $4.18\overline{6}$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 {(6 u n i t s)}^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.3

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

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Step 3.1.1.3.1

Apply the product rule to $6 u n i t s$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 ({(6 u n i t)}^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.3.2

Apply the product rule to $6 u n i t$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 ({(6 u n i)}^{3} t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.3.3

Apply the product rule to $6 u n i$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 ({(6 u n)}^{3} i^{3} t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.3.4

Apply the product rule to $6 u n$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 ({(6 u)}^{3} n^{3} i^{3} t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.3.5

Apply the product rule to $6 u$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 (6^{3} u^{3} n^{3} i^{3} t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.4

Raise $6$ to the power of $3$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 (216 u^{3} n^{3} i^{3} t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.5

Factor out $i^{2}$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 (216 u^{3} n^{3} (i^{2} \cdot i) t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.6

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

$0.2388535 (\frac{4}{3} \cdot (3.14 (216 u^{3} n^{3} (- 1 \cdot i) t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.7

Rewrite $- 1 i$ as $- i$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 (216 u^{3} n^{3} (- i) t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.8

Multiply $- 1$ by $216$ .

$0.2388535 (\frac{4}{3} \cdot (3.14 (- 216 u^{3} n^{3} i t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.9

Multiply $- 216$ by $3.14$ .

$0.2388535 (\frac{4}{3} \cdot (- 678.24 (u^{3} n^{3} i t^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10

Multiply $\frac{4}{3} (- 678.24 u^{3} n^{3} i t^{3} s^{3})$ .

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Step 3.1.1.10.1

Combine $- 678.24$ and $\frac{4}{3}$ .

$0.2388535 (\frac{- 678.24 \cdot 4}{3} (u^{3} n^{3} i t^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.2

Multiply $- 678.24$ by $4$ .

$0.2388535 (\frac{- 2712.96}{3} (u^{3} n^{3} i t^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.3

Combine $u^{3}$ and $\frac{- 2712.96}{3}$ .

$0.2388535 (\frac{u^{3} \cdot - 2712.96}{3} (n^{3} i t^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.4

Combine $n^{3}$ and $\frac{u^{3} \cdot - 2712.96}{3}$ .

$0.2388535 (\frac{n^{3} (u^{3} \cdot - 2712.96)}{3} (i t^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.5

Combine $i$ and $\frac{n^{3} (u^{3} \cdot - 2712.96)}{3}$ .

$0.2388535 (\frac{i (n^{3} (u^{3} \cdot - 2712.96))}{3} (t^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.6

Combine $t^{3}$ and $\frac{i (n^{3} (u^{3} \cdot - 2712.96))}{3}$ .

$0.2388535 (\frac{t^{3} (i (n^{3} (u^{3} \cdot - 2712.96)))}{3} s^{3}) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.10.7

Combine $\frac{t^{3} (i (n^{3} (u^{3} \cdot - 2712.96)))}{3}$ and $s^{3}$ .

$0.2388535 \frac{t^{3} (i (n^{3} (u^{3} \cdot - 2712.96))) s^{3}}{3} = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.11

Simplify the expression.

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Step 3.1.1.11.1

Move $- 2712.96$ to the left of $t^{3} i n^{3} u^{3}$ .

$0.2388535 \frac{- 2712.96 \cdot (t^{3} i n^{3} u^{3}) s^{3}}{3} = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.11.2

Move the negative in front of the fraction.

$0.2388535 (- \frac{2712.96 \cdot t^{3} i n^{3} u^{3} s^{3}}{3}) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.12

Factor $2712.96$ out of $2712.96 \cdot t^{3} i n^{3} u^{3} s^{3}$ .

$0.2388535 (- \frac{2712.96 (t^{3} i n^{3} u^{3} s^{3})}{3}) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.13

Factor $3$ out of $3$ .

$0.2388535 (- \frac{2712.96 (t^{3} i n^{3} u^{3} s^{3})}{3 (1)}) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.14

Separate fractions.

$0.2388535 (- (\frac{2712.96}{3} \cdot \frac{t^{3} i n^{3} u^{3} s^{3}}{1})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.15

Divide $2712.96$ by $3$ .

$0.2388535 (- (904.32 \frac{t^{3} i n^{3} u^{3} s^{3}}{1})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.16

Divide $t^{3} i n^{3} u^{3} s^{3}$ by $1$ .

$0.2388535 (- (904.32 (t^{3} i n^{3} u^{3} s^{3}))) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.17

Multiply $904.32$ by $- 1$ .

$0.2388535 (- 904.32 (t^{3} i n^{3} u^{3} s^{3})) = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.1.1.18

Multiply $- 904.32$ by $0.2388535$ .

$- 216 t^{3} i n^{3} u^{3} s^{3} = \frac{1}{\frac{4}{3} \cdot 3.14} v$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{4}{3} \cdot 3.14} v$ .

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Step 3.2.1.1

Combine $\frac{4}{3}$ and $3.14$ .

$- 216 t^{3} i n^{3} u^{3} s^{3} = \frac{1}{\frac{4 \cdot 3.14}{3}} v$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Multiply $4$ by $3.14$ .

$- 216 t^{3} i n^{3} u^{3} s^{3} = \frac{1}{\frac{12.56}{3}} v$

Step 3.2.1.2.2

Divide $12.56$ by $3$ .

$- 216 t^{3} i n^{3} u^{3} s^{3} = \frac{1}{4.18\overline{6}} v$

Step 3.2.1.2.3

Divide $1$ by $4.18\overline{6}$ .

$- 216 t^{3} i n^{3} u^{3} s^{3} = 0.2388535 v$

Step 4

Divide each term in $- 216 t^{3} i n^{3} u^{3} s^{3} = 0.2388535 v$ by $- 216 i n^{3} u^{3} s^{3}$ and simplify.

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Step 4.1

Divide each term in $- 216 t^{3} i n^{3} u^{3} s^{3} = 0.2388535 v$ by $- 216 i n^{3} u^{3} s^{3}$ .

$\frac{- 216 t^{3} i n^{3} u^{3} s^{3}}{- 216 i n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 216$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 216 t^{3} i n^{3} u^{3} s^{3}}{- 216 i n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.1.2

Rewrite the expression.

$\frac{t^{3} i n^{3} u^{3} s^{3}}{i n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.2

Cancel the common factor of $i$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{t^{3} i n^{3} u^{3} s^{3}}{i n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.2.2

Rewrite the expression.

$\frac{t^{3} n^{3} u^{3} s^{3}}{n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.3

Cancel the common factor of $n^{3}$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{t^{3} n^{3} u^{3} s^{3}}{n^{3} u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.3.2

Rewrite the expression.

$\frac{t^{3} u^{3} s^{3}}{u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.4

Cancel the common factor of $u^{3}$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{t^{3} u^{3} s^{3}}{u^{3} s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.4.2

Rewrite the expression.

$\frac{t^{3} s^{3}}{s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.5

Cancel the common factor of $s^{3}$ .

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Step 4.2.5.1

Cancel the common factor.

$\frac{t^{3} s^{3}}{s^{3}} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.2.5.2

Divide $t^{3}$ by $1$ .

$t^{3} = \frac{0.2388535 v}{- 216 i n^{3} u^{3} s^{3}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$t^{3} = - \frac{0.2388535 v}{216 i n^{3} u^{3} s^{3}}$

Step 4.3.2

Factor $0.2388535$ out of $0.2388535 v$ .

$t^{3} = - \frac{0.2388535 (v)}{216 i n^{3} u^{3} s^{3}}$

Step 4.3.3

Factor $216$ out of $216 i n^{3} u^{3} s^{3}$ .

$t^{3} = - \frac{0.2388535 (v)}{216 (i n^{3} u^{3} s^{3})}$

Step 4.3.4

Separate fractions.

$t^{3} = - (\frac{0.2388535}{216} \cdot \frac{v}{i n^{3} u^{3} s^{3}})$

Step 4.3.5

Divide $0.2388535$ by $216$ .

$t^{3} = - (0.0011058 \frac{v}{i n^{3} u^{3} s^{3}})$

Step 4.3.6

Combine $0.0011058$ and $\frac{v}{i n^{3} u^{3} s^{3}}$ .

$t^{3} = - \frac{0.0011058 v}{i n^{3} u^{3} s^{3}}$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \sqrt[3]{- \frac{0.0011058 v}{i n^{3} u^{3} s^{3}}}$

Step 6

Simplify $\sqrt[3]{- \frac{0.0011058 v}{i n^{3} u^{3} s^{3}}}$ .

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Step 6.1

Rewrite $- \frac{0.0011058 v}{i n^{3} u^{3} s^{3}}$ as ${(- \frac{1}{n u s})}^{3} \frac{0.0011058 v}{i}$ .

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Step 6.1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$t = \sqrt[3]{{(- 1)}^{3} \frac{0.0011058 v}{i n^{3} u^{3} s^{3}}}$

Step 6.1.2

Factor the perfect power $1^{3}$ out of $0.0011058 v$ .

$t = \sqrt[3]{{(- 1)}^{3} \frac{1^{3} (0.0011058 v)}{i n^{3} u^{3} s^{3}}}$

Step 6.1.3

Factor the perfect power ${(n u s)}^{3}$ out of $i n^{3} u^{3} s^{3}$ .

$t = \sqrt[3]{{(- 1)}^{3} \frac{1^{3} (0.0011058 v)}{{(n u s)}^{3} i}}$

Step 6.1.4

Rearrange the fraction $\frac{1^{3} (0.0011058 v)}{{(n u s)}^{3} i}$ .

$t = \sqrt[3]{{(- 1)}^{3} ({(\frac{1}{n u s})}^{3} \frac{0.0011058 v}{i})}$

Step 6.1.5

Rewrite ${(- 1)}^{3} {(\frac{1}{n u s})}^{3}$ as ${(- \frac{1}{n u s})}^{3}$ .

$t = \sqrt[3]{{(- \frac{1}{n u s})}^{3} \frac{0.0011058 v}{i}}$

Step 6.2

Pull terms out from under the radical.

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v}{i}}$

Step 6.3

Multiply the numerator and denominator of $\frac{0.0011058 v}{i}$ by the conjugate of $i$ to make the denominator real.

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v}{i} \cdot \frac{i}{i}}$

Step 6.4

Multiply.

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Step 6.4.1

Combine.

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{i i}}$

Step 6.4.2

Simplify the denominator.

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Step 6.4.2.1

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

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{i^{1} i}}$

Step 6.4.2.2

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

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{i^{1} i^{1}}}$

Step 6.4.2.3

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

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{i^{1 + 1}}}$

Step 6.4.2.4

Add $1$ and $1$ .

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{i^{2}}}$

Step 6.4.2.5

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

$t = - \frac{1}{n u s} \sqrt[3]{\frac{0.0011058 v i}{- 1}}$

Step 6.5

Move the negative one from the denominator of $\frac{0.0011058 v i}{- 1}$ .

$t = - \frac{1}{n u s} \sqrt[3]{- 1 \cdot (0.0011058 v i)}$

Step 6.6

Rewrite $- 1 \cdot (0.0011058 v i)$ as $- (0.0011058 v i)$ .

$t = - \frac{1}{n u s} \sqrt[3]{- (0.0011058 v i)}$

Step 6.7

Multiply $0.0011058$ by $- 1$ .

$t = - \frac{1}{n u s} \sqrt[3]{- 0.0011058 (v i)}$

Step 6.8

Rewrite $- 0.0011058 v i$ as ${({(- 1)}^{3})}^{3} \cdot (0.0011058 v i)$ .

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Step 6.8.1

Rewrite.

$t = - \frac{1}{n u s} \sqrt[3]{- 1 \cdot 0.0011058 v i}$

Step 6.8.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$t = - \frac{1}{n u s} \sqrt[3]{{(- 1)}^{3} \cdot 0.0011058 v i}$

Step 6.8.3

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$t = - \frac{1}{n u s} \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot 0.0011058 v i}$

Step 6.8.4

Add parentheses.

$t = - \frac{1}{n u s} \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot 0.0011058 (v i)}$

Step 6.8.5

Add parentheses.

$t = - \frac{1}{n u s} \sqrt[3]{{({(- 1)}^{3})}^{3} \cdot (0.0011058 v i)}$

Step 6.9

Pull terms out from under the radical.

$t = - \frac{1}{n u s} ({(- 1)}^{3} \sqrt[3]{0.0011058 v i})$

Step 6.10

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

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Step 6.10.1

Move ${(- 1)}^{3}$ .

$t = {(- 1)}^{3} \cdot - 1 \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.10.2

Multiply ${(- 1)}^{3}$ by $- 1$ .

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Step 6.10.2.1

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

$t = {(- 1)}^{3} \cdot {(- 1)}^{1} \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.10.2.2

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

$t = {(- 1)}^{3 + 1} \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.10.3

Add $3$ and $1$ .

$t = {(- 1)}^{4} \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.11

Simplify the expression.

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Step 6.11.1

Raise $- 1$ to the power of $4$ .

$t = 1 \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.11.2

Multiply $\frac{1}{n u s}$ by $1$ .

$t = \frac{1}{n u s} \sqrt[3]{0.0011058 v i}$

Step 6.12

Combine $\frac{1}{n u s}$ and $\sqrt[3]{0.0011058 v i}$ .

$t = \frac{\sqrt[3]{0.0011058 v i}}{n u s}$