Basic Math Examples

$\frac{10}{\sqrt[3]{5}}$

Step 1

Multiply $\frac{10}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$\frac{10}{\sqrt[3]{5}} \cdot \frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{10}{\sqrt[3]{5}}$ by $\frac{{\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{2}}$ .

$\frac{10 {\sqrt[3]{5}}^{2}}{\sqrt[3]{5} {\sqrt[3]{5}}^{2}}$

Step 2.2

Raise $\sqrt[3]{5}$ to the power of $1$ .

$\frac{10 {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{2}}$

Step 2.3

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

$\frac{10 {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{1 + 2}}$

Step 2.4

Add $1$ and $2$ .

$\frac{10 {\sqrt[3]{5}}^{2}}{{\sqrt[3]{5}}^{3}}$

Step 2.5

Rewrite ${\sqrt[3]{5}}^{3}$ as $5$ .

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Step 2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$\frac{10 {\sqrt[3]{5}}^{2}}{{(5^{\frac{1}{3}})}^{3}}$

Step 2.5.2

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

$\frac{10 {\sqrt[3]{5}}^{2}}{5^{\frac{1}{3} \cdot 3}}$

Step 2.5.3

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

$\frac{10 {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 2.5.4

Cancel the common factor of $3$ .

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Step 2.5.4.1

Cancel the common factor.

$\frac{10 {\sqrt[3]{5}}^{2}}{5^{\frac{3}{3}}}$

Step 2.5.4.2

Rewrite the expression.

$\frac{10 {\sqrt[3]{5}}^{2}}{5^{1}}$

Step 2.5.5

Evaluate the exponent.

$\frac{10 {\sqrt[3]{5}}^{2}}{5}$

Step 3

Cancel the common factor of $10$ and $5$ .

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Step 3.1

Factor $5$ out of $10 {\sqrt[3]{5}}^{2}$ .

$\frac{5 (2 {\sqrt[3]{5}}^{2})}{5}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $5$ .

$\frac{5 (2 {\sqrt[3]{5}}^{2})}{5 (1)}$

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{2 {\sqrt[3]{5}}^{2}}{1}$

Step 3.2.4

Divide $2 {\sqrt[3]{5}}^{2}$ by $1$ .

$2 {\sqrt[3]{5}}^{2}$

Step 4

Rewrite ${\sqrt[3]{5}}^{2}$ as $\sqrt[3]{5^{2}}$ .

$2 \sqrt[3]{5^{2}}$

Step 5

Raise $5$ to the power of $2$ .

$2 \sqrt[3]{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{25}$

Decimal Form:

$5.84803547 \dots$