Simplify 6 square root of 3* square root of 3*4 square root of 4

$6 \sqrt{3} \cdot \sqrt{3} \cdot 4 \sqrt{4}$

Multiply $6 \sqrt{3} \sqrt{3}$ .

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

$6 ({\sqrt{3}}^{1} \sqrt{3}) \cdot (4 \sqrt{4})$

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

$6 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) \cdot (4 \sqrt{4})$

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

$6 {\sqrt{3}}^{1 + 1} \cdot (4 \sqrt{4})$

Add $1$ and $1$ .

$6 {\sqrt{3}}^{2} \cdot (4 \sqrt{4})$

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

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

$6 {(3^{\frac{1}{2}})}^{2} \cdot (4 \sqrt{4})$

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

$6 \cdot 3^{\frac{1}{2} \cdot 2} \cdot (4 \sqrt{4})$

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

$6 \cdot 3^{\frac{2}{2}} \cdot (4 \sqrt{4})$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 \cdot 3^{\frac{2}{2}} \cdot (4 \sqrt{4})$

Rewrite the expression.

$6 \cdot 3^{1} \cdot (4 \sqrt{4})$

Evaluate the exponent.

$6 \cdot 3 \cdot (4 \sqrt{4})$

Write the expression using exponents.

Multiply $6$ by $3$ .

$18 \cdot (4 \sqrt{4})$

Rewrite $4$ as $2^{2}$ .

$18 \cdot (4 \sqrt{2^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$18 \cdot (4 \cdot 2)$

Multiply $4$ by $2$ .

$18 \cdot 8$

Multiply $18$ by $8$ .

$144$