Basic Math Examples

$\frac{2}{5} \div (- \frac{279 \sqrt[4]{2}}{- 14})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{5} (- \frac{- 14}{279 \sqrt[4]{2}})$

Step 2

Move the negative in front of the fraction.

$\frac{2}{5} (- - \frac{14}{279 \sqrt[4]{2}})$

Step 3

Multiply $\frac{14}{279 \sqrt[4]{2}}$ by $\frac{{\sqrt[4]{2}}^{3}}{{\sqrt[4]{2}}^{3}}$ .

$\frac{2}{5} (- - (\frac{14}{279 \sqrt[4]{2}} \cdot \frac{{\sqrt[4]{2}}^{3}}{{\sqrt[4]{2}}^{3}}))$

Step 4

Simplify terms.

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Step 4.1

Combine and simplify the denominator.

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Step 4.1.1

Multiply $\frac{14}{279 \sqrt[4]{2}}$ by $\frac{{\sqrt[4]{2}}^{3}}{{\sqrt[4]{2}}^{3}}$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \sqrt[4]{2} {\sqrt[4]{2}}^{3}})$

Step 4.1.2

Move $\sqrt[4]{2}$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 (\sqrt[4]{2} {\sqrt[4]{2}}^{3})})$

Step 4.1.3

Raise $\sqrt[4]{2}$ to the power of $1$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 ({\sqrt[4]{2}}^{1} {\sqrt[4]{2}}^{3})})$

Step 4.1.4

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

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 {\sqrt[4]{2}}^{1 + 3}})$

Step 4.1.5

Add $1$ and $3$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 {\sqrt[4]{2}}^{4}})$

Step 4.1.6

Rewrite ${\sqrt[4]{2}}^{4}$ as $2$ .

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Step 4.1.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2}$ as $2^{\frac{1}{4}}$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 {(2^{\frac{1}{4}})}^{4}})$

Step 4.1.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \cdot 2^{\frac{1}{4} \cdot 4}})$

Step 4.1.6.3

Combine $\frac{1}{4}$ and $4$ .

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \cdot 2^{\frac{4}{4}}})$

Step 4.1.6.4

Cancel the common factor of $4$ .

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Step 4.1.6.4.1

Cancel the common factor.

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \cdot 2^{\frac{4}{4}}})$

Step 4.1.6.4.2

Rewrite the expression.

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \cdot 2^{1}})$

Step 4.1.6.5

Evaluate the exponent.

$\frac{2}{5} (- - \frac{14 {\sqrt[4]{2}}^{3}}{279 \cdot 2})$

Step 4.2

Cancel the common factor of $14$ and $2$ .

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Step 4.2.1

Factor $2$ out of $14 {\sqrt[4]{2}}^{3}$ .

$\frac{2}{5} (- - \frac{2 (7 {\sqrt[4]{2}}^{3})}{279 \cdot 2})$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $2$ out of $279 \cdot 2$ .

$\frac{2}{5} (- - \frac{2 (7 {\sqrt[4]{2}}^{3})}{2 \cdot 279})$

Step 4.2.2.2

Cancel the common factor.

$\frac{2}{5} (- - \frac{2 (7 {\sqrt[4]{2}}^{3})}{2 \cdot 279})$

Step 4.2.2.3

Rewrite the expression.

$\frac{2}{5} (- - \frac{7 {\sqrt[4]{2}}^{3}}{279})$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite ${\sqrt[4]{2}}^{3}$ as $\sqrt[4]{2^{3}}$ .

$\frac{2}{5} (- - \frac{7 \sqrt[4]{2^{3}}}{279})$

Step 5.2

Raise $2$ to the power of $3$ .

$\frac{2}{5} (- - \frac{7 \sqrt[4]{8}}{279})$

Step 6

Multiply $- - \frac{7 \sqrt[4]{8}}{279}$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

$\frac{2}{5} (1 \frac{7 \sqrt[4]{8}}{279})$

Step 6.2

Multiply $\frac{7 \sqrt[4]{8}}{279}$ by $1$ .

$\frac{2}{5} \cdot \frac{7 \sqrt[4]{8}}{279}$

Step 7

Multiply $\frac{2}{5} \cdot \frac{7 \sqrt[4]{8}}{279}$ .

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Step 7.1

Multiply $\frac{2}{5}$ by $\frac{7 \sqrt[4]{8}}{279}$ .

$\frac{2 (7 \sqrt[4]{8})}{5 \cdot 279}$

Step 7.2

Multiply $7$ by $2$ .

$\frac{14 \sqrt[4]{8}}{5 \cdot 279}$

Step 7.3

Multiply $5$ by $279$ .

$\frac{14 \sqrt[4]{8}}{1395}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{14 \sqrt[4]{8}}{1395}$

Decimal Form:

$0.01687820 \dots$