Basic Math Examples

$4 \sqrt[3]{\frac{56}{24}}$

Step 1

Cancel the common factor of $56$ and $24$ .

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Step 1.1

Factor $8$ out of $56$ .

$4 \sqrt[3]{\frac{8 (7)}{24}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $24$ .

$4 \sqrt[3]{\frac{8 \cdot 7}{8 \cdot 3}}$

Step 1.2.2

Cancel the common factor.

$4 \sqrt[3]{\frac{8 \cdot 7}{8 \cdot 3}}$

Step 1.2.3

Rewrite the expression.

$4 \sqrt[3]{\frac{7}{3}}$

Step 2

Rewrite $\sqrt[3]{\frac{7}{3}}$ as $\frac{\sqrt[3]{7}}{\sqrt[3]{3}}$ .

$4 \frac{\sqrt[3]{7}}{\sqrt[3]{3}}$

Step 3

Multiply $\frac{\sqrt[3]{7}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

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

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{\sqrt[3]{7}}{\sqrt[3]{3}}$ by $\frac{{\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{2}}$ .

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{\sqrt[3]{3} {\sqrt[3]{3}}^{2}}$

Step 4.2

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

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{2}}$

Step 4.3

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

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

Step 4.4

Add $1$ and $2$ .

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{{\sqrt[3]{3}}^{3}}$

Step 4.5

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

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Step 4.5.1

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

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

Step 4.5.2

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

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

Step 4.5.3

Combine $\frac{1}{3}$ and $3$ .

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Step 4.5.4

Cancel the common factor of $3$ .

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Step 4.5.4.1

Cancel the common factor.

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{3^{\frac{3}{3}}}$

Step 4.5.4.2

Rewrite the expression.

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{3^{1}}$

Step 4.5.5

Evaluate the exponent.

$4 \frac{\sqrt[3]{7} {\sqrt[3]{3}}^{2}}{3}$

Step 5

Simplify the numerator.

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Step 5.1

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

$4 \frac{\sqrt[3]{7} \sqrt[3]{3^{2}}}{3}$

Step 5.2

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

$4 \frac{\sqrt[3]{7} \sqrt[3]{9}}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Combine using the product rule for radicals.

$4 \frac{\sqrt[3]{7 \cdot 9}}{3}$

Step 6.2

Multiply $7$ by $9$ .

$4 \frac{\sqrt[3]{63}}{3}$

Step 7

Combine $4$ and $\frac{\sqrt[3]{63}}{3}$ .

$\frac{4 \sqrt[3]{63}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt[3]{63}}{3}$

Decimal Form:

$5.30540961 \dots$