Finite Math Examples

$\frac{4}{\sqrt[4]{552}}$

Step 1

Multiply $\frac{4}{\sqrt[4]{552}}$ by $\frac{{\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{3}}$ .

$\frac{4}{\sqrt[4]{552}} \cdot \frac{{\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{3}}$

Step 2

Simplify terms.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{4}{\sqrt[4]{552}}$ by $\frac{{\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{3}}$ .

$\frac{4 {\sqrt[4]{552}}^{3}}{\sqrt[4]{552} {\sqrt[4]{552}}^{3}}$

Step 2.1.2

Raise $\sqrt[4]{552}$ to the power of $1$ .

$\frac{4 {\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{1} {\sqrt[4]{552}}^{3}}$

Step 2.1.3

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

$\frac{4 {\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{1 + 3}}$

Step 2.1.4

Add $1$ and $3$ .

$\frac{4 {\sqrt[4]{552}}^{3}}{{\sqrt[4]{552}}^{4}}$

Step 2.1.5

Rewrite ${\sqrt[4]{552}}^{4}$ as $552$ .

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Step 2.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{552}$ as $552^{\frac{1}{4}}$ .

$\frac{4 {\sqrt[4]{552}}^{3}}{{(552^{\frac{1}{4}})}^{4}}$

Step 2.1.5.2

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

$\frac{4 {\sqrt[4]{552}}^{3}}{552^{\frac{1}{4} \cdot 4}}$

Step 2.1.5.3

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

$\frac{4 {\sqrt[4]{552}}^{3}}{552^{\frac{4}{4}}}$

Step 2.1.5.4

Cancel the common factor of $4$ .

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Step 2.1.5.4.1

Cancel the common factor.

$\frac{4 {\sqrt[4]{552}}^{3}}{552^{\frac{4}{4}}}$

Step 2.1.5.4.2

Rewrite the expression.

$\frac{4 {\sqrt[4]{552}}^{3}}{552^{1}}$

Step 2.1.5.5

Evaluate the exponent.

$\frac{4 {\sqrt[4]{552}}^{3}}{552}$

Step 2.2

Cancel the common factor of $4$ and $552$ .

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Step 2.2.1

Factor $4$ out of $4 {\sqrt[4]{552}}^{3}$ .

$\frac{4 ({\sqrt[4]{552}}^{3})}{552}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $4$ out of $552$ .

$\frac{4 {\sqrt[4]{552}}^{3}}{4 \cdot 138}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 {\sqrt[4]{552}}^{3}}{4 \cdot 138}$

Step 2.2.2.3

Rewrite the expression.

$\frac{{\sqrt[4]{552}}^{3}}{138}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[4]{552}}^{3}$ as $\sqrt[4]{552^{3}}$ .

$\frac{\sqrt[4]{552^{3}}}{138}$

Step 3.2

Raise $552$ to the power of $3$ .

$\frac{\sqrt[4]{168196608}}{138}$

Step 3.3

Rewrite $168196608$ as $4^{4} \cdot 657018$ .

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Step 3.3.1

Factor $256$ out of $168196608$ .

$\frac{\sqrt[4]{256 (657018)}}{138}$

Step 3.3.2

Rewrite $256$ as $4^{4}$ .

$\frac{\sqrt[4]{4^{4} \cdot 657018}}{138}$

Step 3.4

Pull terms out from under the radical.

$\frac{4 \sqrt[4]{657018}}{138}$

Step 4

Cancel the common factor of $4$ and $138$ .

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Step 4.1

Factor $2$ out of $4 \sqrt[4]{657018}$ .

$\frac{2 (2 \sqrt[4]{657018})}{138}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $138$ .

$\frac{2 (2 \sqrt[4]{657018})}{2 (69)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (2 \sqrt[4]{657018})}{2 \cdot 69}$

Step 4.2.3

Rewrite the expression.

$\frac{2 \sqrt[4]{657018}}{69}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt[4]{657018}}{69}$

Decimal Form:

$0.82523040 \dots$