Simplify fourth root of 6*3 fourth root of 6

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

Multiply $\sqrt[4]{6} (3 \sqrt[4]{6})$ .

Raise $\sqrt[4]{6}$ to the power of $1$ .

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

Raise $\sqrt[4]{6}$ to the power of $1$ .

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

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

$3 {\sqrt[4]{6}}^{1 + 1}$

Add $1$ and $1$ .

$3 {\sqrt[4]{6}}^{2}$

Rewrite ${\sqrt[4]{6}}^{2}$ as $\sqrt{6}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{6}$ as $6^{\frac{1}{4}}$ .

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

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

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

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

$3 \cdot 6^{\frac{2}{4}}$

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$3 \cdot 6^{\frac{2 \cdot 1}{2 \cdot 2}}$

Cancel the common factor.

$3 \cdot 6^{\frac{2 \cdot 1}{2 \cdot 2}}$

Rewrite the expression.

$3 \cdot 6^{\frac{1}{2}}$

Rewrite $6^{\frac{1}{2}}$ as $\sqrt{6}$ .

$3 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{6}$

Decimal Form:

$7.34846922 \dots$