Evaluate 4/( cube root of 36)

$\frac{4}{\sqrt[3]{36}}$

Step 1

Multiply $\frac{4}{\sqrt[3]{36}}$ by $\frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$ .

$\frac{4}{\sqrt[3]{36}} \cdot \frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$

Step 2

Simplify terms.

Combine and simplify the denominator.

Multiply $\frac{4}{\sqrt[3]{36}}$ by $\frac{{\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{2}}$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{\sqrt[3]{36} {\sqrt[3]{36}}^{2}}$

Raise $\sqrt[3]{36}$ to the power of $1$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{1} {\sqrt[3]{36}}^{2}}$

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

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{\sqrt[3]{36}}^{3}}$

Rewrite ${\sqrt[3]{36}}^{3}$ as $36$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{36}$ as $36^{\frac{1}{3}}$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{{(36^{\frac{1}{3}})}^{3}}$

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

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{1}{3} \cdot 3}}$

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

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{4 {\sqrt[3]{36}}^{2}}{36^{1}}$

Evaluate the exponent.

$\frac{4 {\sqrt[3]{36}}^{2}}{36}$

Cancel the common factor of $4$ and $36$ .

Factor $4$ out of $4 {\sqrt[3]{36}}^{2}$ .

$\frac{4 ({\sqrt[3]{36}}^{2})}{36}$

Cancel the common factors.

Factor $4$ out of $36$ .

$\frac{4 {\sqrt[3]{36}}^{2}}{4 \cdot 9}$

Cancel the common factor.

$\frac{4 {\sqrt[3]{36}}^{2}}{4 \cdot 9}$

Rewrite the expression.

$\frac{{\sqrt[3]{36}}^{2}}{9}$

Step 3

Simplify the numerator.

Rewrite ${\sqrt[3]{36}}^{2}$ as $\sqrt[3]{36^{2}}$ .

$\frac{\sqrt[3]{36^{2}}}{9}$

Raise $36$ to the power of $2$ .

$\frac{\sqrt[3]{1296}}{9}$

Rewrite $1296$ as $6^{3} \cdot 6$ .

Factor $216$ out of $1296$ .

$\frac{\sqrt[3]{216 (6)}}{9}$

Rewrite $216$ as $6^{3}$ .

$\frac{\sqrt[3]{6^{3} \cdot 6}}{9}$

Pull terms out from under the radical.

$\frac{6 \sqrt[3]{6}}{9}$

Step 4

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6 \sqrt[3]{6}$ .

$\frac{3 (2 \sqrt[3]{6})}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 \sqrt[3]{6}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt[3]{6}}{3}$

Decimal Form:

$1.21141372 \dots$

Evaluate 4/( cube root of 36)

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