Basic Math Examples

$| \sqrt[4]{3} - 7 | \cdot (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 1

$\sqrt[4]{3} - 7$ is approximately $- 5.68392598$ which is negative so negate $\sqrt[4]{3} - 7$ and remove the absolute value

$- (\sqrt[4]{3} - 7) \cdot (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 2

Apply the distributive property.

$(- \sqrt[4]{3} - - 7) \cdot (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 3

Multiply $- 1$ by $- 7$ .

$(- \sqrt[4]{3} + 7) \cdot (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 4

Expand $(- \sqrt[4]{3} + 7) (\sqrt[4]{3} - 7)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$- \sqrt[4]{3} (\sqrt[4]{3} - 7) + 7 (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 4.2

Apply the distributive property.

$- \sqrt[4]{3} \sqrt[4]{3} - \sqrt[4]{3} \cdot - 7 + 7 (\sqrt[4]{3} - 7) - \sqrt[56]{3}$

Step 4.3

Apply the distributive property.

$- \sqrt[4]{3} \sqrt[4]{3} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $- \sqrt[4]{3} \sqrt[4]{3}$ .

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Step 5.1.1.1

Raise $\sqrt[4]{3}$ to the power of $1$ .

$- ({\sqrt[4]{3}}^{1} \sqrt[4]{3}) - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.1.2

Raise $\sqrt[4]{3}$ to the power of $1$ .

$- ({\sqrt[4]{3}}^{1} {\sqrt[4]{3}}^{1}) - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.1.3

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

$- {\sqrt[4]{3}}^{1 + 1} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.1.4

Add $1$ and $1$ .

$- {\sqrt[4]{3}}^{2} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2

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

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Step 5.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{3}$ as $3^{\frac{1}{4}}$ .

$- {(3^{\frac{1}{4}})}^{2} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.2

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

$- 3^{\frac{1}{4} \cdot 2} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.3

Combine $\frac{1}{4}$ and $2$ .

$- 3^{\frac{2}{4}} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.4

Cancel the common factor of $2$ and $4$ .

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Step 5.1.2.4.1

Factor $2$ out of $2$ .

$- 3^{\frac{2 (1)}{4}} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.4.2

Cancel the common factors.

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Step 5.1.2.4.2.1

Factor $2$ out of $4$ .

$- 3^{\frac{2 \cdot 1}{2 \cdot 2}} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.4.2.2

Cancel the common factor.

$- 3^{\frac{2 \cdot 1}{2 \cdot 2}} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.4.2.3

Rewrite the expression.

$- 3^{\frac{1}{2}} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.2.5

Rewrite $3^{\frac{1}{2}}$ as $\sqrt{3}$ .

$- \sqrt{3} - \sqrt[4]{3} \cdot - 7 + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.3

Multiply $- 7$ by $- 1$ .

$- \sqrt{3} + 7 \sqrt[4]{3} + 7 \sqrt[4]{3} + 7 \cdot - 7 - \sqrt[56]{3}$

Step 5.1.4

Multiply $7$ by $- 7$ .

$- \sqrt{3} + 7 \sqrt[4]{3} + 7 \sqrt[4]{3} - 49 - \sqrt[56]{3}$

Step 5.2

Add $7 \sqrt[4]{3}$ and $7 \sqrt[4]{3}$ .

$- \sqrt{3} + 14 \sqrt[4]{3} - 49 - \sqrt[56]{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3} + 14 \sqrt[4]{3} - 49 - \sqrt[56]{3}$

Decimal Form:

$- 33.32682640 \dots$