Basic Math Examples

$(\sqrt[3]{3}) {(\sqrt[4]{3})}^{12}$

Step 1

Rewrite ${\sqrt[4]{3}}^{12}$ as $3^{3}$ .

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Step 1.1

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

$\sqrt[3]{3} {(3^{\frac{1}{4}})}^{12}$

Step 1.2

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

$\sqrt[3]{3} \cdot 3^{\frac{1}{4} \cdot 12}$

Step 1.3

Combine $\frac{1}{4}$ and $12$ .

$\sqrt[3]{3} \cdot 3^{\frac{12}{4}}$

Step 1.4

Cancel the common factor of $12$ and $4$ .

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Step 1.4.1

Factor $4$ out of $12$ .

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

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $4$ out of $4$ .

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

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 1.4.2.4

Divide $3$ by $1$ .

$\sqrt[3]{3} \cdot 3^{3}$

Step 2

Simplify the expression.

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Step 2.1

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

$\sqrt[3]{3} \cdot 27$

Step 2.2

Move $27$ to the left of $\sqrt[3]{3}$ .

$27 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$27 \sqrt[3]{3}$

Decimal Form:

$38.94073839 \dots$