Simplify the Radical Expression (2 cube root of 3)^3

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

Step 1

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

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

Step 2

Raise $2$ to the power of $3$ .

$8 {\sqrt[3]{3}}^{3}$

Step 3

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

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

$8 {(3^{\frac{1}{3}})}^{3}$

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

$8 \cdot 3^{\frac{1}{3} \cdot 3}$

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

$8 \cdot 3^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 \cdot 3^{\frac{3}{3}}$

Rewrite the expression.

$8 \cdot 3^{1}$

Evaluate the exponent.

$8 \cdot 3$

Step 4

Multiply $8$ by $3$ .

$24$