Simplify (2 square root of 3)^4

${(2 \sqrt{3})}^{4}$

Step 1

Simplify the expression.

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

$2^{4} {\sqrt{3}}^{4}$

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

$16 {\sqrt{3}}^{4}$

Step 2

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

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

$16 {(3^{\frac{1}{2}})}^{4}$

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

$16 \cdot 3^{\frac{1}{2} \cdot 4}$

Combine $\frac{1}{2}$ and $4$ .

$16 \cdot 3^{\frac{4}{2}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

$16 \cdot 3^{\frac{2 \cdot 2}{2}}$

Cancel the common factors.

Factor $2$ out of $2$ .

$16 \cdot 3^{\frac{2 \cdot 2}{2 (1)}}$

Cancel the common factor.

$16 \cdot 3^{\frac{2 \cdot 2}{2 \cdot 1}}$

Rewrite the expression.

$16 \cdot 3^{\frac{2}{1}}$

Divide $2$ by $1$ .

$16 \cdot 3^{2}$

Step 3

Simplify the expression.

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

$16 \cdot 9$

Multiply $16$ by $9$ .

$144$