Basic Math Examples

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

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Step 2.1

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

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

Step 2.2

Move $\sqrt[3]{4}$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $2$ .

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

Step 2.6

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

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Step 2.6.1

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

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

Step 2.6.2

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

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

Step 2.6.3

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

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

Step 2.6.4

Cancel the common factor of $3$ .

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Step 2.6.4.1

Cancel the common factor.

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

Step 2.6.4.2

Rewrite the expression.

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

Step 2.6.5

Evaluate the exponent.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Raise $4$ to the power of $2$ .

$\frac{(2 + \sqrt[3]{4}) \sqrt[3]{16}}{3 \cdot 4}$

Step 3.3

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 3.3.1

Factor $8$ out of $16$ .

$\frac{(2 + \sqrt[3]{4}) \sqrt[3]{8 (2)}}{3 \cdot 4}$

Step 3.3.2

Rewrite $8$ as $2^{3}$ .

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

Step 3.4

Pull terms out from under the radical.

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply $3$ by $4$ .

$\frac{(2 + \sqrt[3]{4}) \cdot 2 \sqrt[3]{2}}{12}$

Step 4.2

Cancel the common factor of $2$ and $12$ .

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Step 4.2.1

Factor $2$ out of $(2 + \sqrt[3]{4}) \cdot 2 \sqrt[3]{2}$ .

$\frac{2 ((2 + \sqrt[3]{4}) \sqrt[3]{2})}{12}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $2$ out of $12$ .

$\frac{2 ((2 + \sqrt[3]{4}) \sqrt[3]{2})}{2 \cdot 6}$

Step 4.2.2.2

Cancel the common factor.

$\frac{2 ((2 + \sqrt[3]{4}) \sqrt[3]{2})}{2 \cdot 6}$

Step 4.2.2.3

Rewrite the expression.

$\frac{(2 + \sqrt[3]{4}) \sqrt[3]{2}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{(2 + \sqrt[3]{4}) \sqrt[3]{2}}{6}$

Decimal Form:

$0.75330701 \dots$