Evaluate (3 cube root of 2)^3

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

Step 1

Simplify the expression.

Apply the product rule to $3 \sqrt[3]{2}$ .

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

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

$27 {\sqrt[3]{2}}^{3}$

Step 2

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$27 {(2^{\frac{1}{3}})}^{3}$

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

$27 \cdot 2^{\frac{1}{3} \cdot 3}$

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

$27 \cdot 2^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 \cdot 2^{\frac{3}{3}}$

Rewrite the expression.

$27 \cdot 2^{1}$

Evaluate the exponent.

$27 \cdot 2$

Step 3

Multiply $27$ by $2$ .

$54$