Simplify (2 square root of 3-x)/(4 cube root of 3-x)

$\frac{2 \sqrt{3 - x}}{4 \sqrt[3]{3 - x}}$

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

Factor $2$ out of $2 \sqrt{3 - x}$ .

$\frac{2 (\sqrt{3 - x})}{4 \sqrt[3]{3 - x}}$

Cancel the common factors.

Factor $2$ out of $4 \sqrt[3]{3 - x}$ .

$\frac{2 (\sqrt{3 - x})}{2 (2 \sqrt[3]{3 - x})}$

Cancel the common factor.

$\frac{2 \sqrt{3 - x}}{2 (2 \sqrt[3]{3 - x})}$

Rewrite the expression.

$\frac{\sqrt{3 - x}}{2 \sqrt[3]{3 - x}}$

Multiply $\frac{\sqrt{3 - x}}{2 \sqrt[3]{3 - x}}$ by $\frac{{\sqrt[3]{3 - x}}^{2}}{{\sqrt[3]{3 - x}}^{2}}$ .

$\frac{\sqrt{3 - x}}{2 \sqrt[3]{3 - x}} \cdot \frac{{\sqrt[3]{3 - x}}^{2}}{{\sqrt[3]{3 - x}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3 - x}}{2 \sqrt[3]{3 - x}}$ by $\frac{{\sqrt[3]{3 - x}}^{2}}{{\sqrt[3]{3 - x}}^{2}}$ .

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 \sqrt[3]{3 - x} {\sqrt[3]{3 - x}}^{2}}$

Move $\sqrt[3]{3 - x}$ .

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

Raise $\sqrt[3]{3 - x}$ to the power of $1$ .

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 ({\sqrt[3]{3 - x}}^{1} {\sqrt[3]{3 - x}}^{2})}$

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

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 {\sqrt[3]{3 - x}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 {\sqrt[3]{3 - x}}^{3}}$

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

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

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 {({(3 - x)}^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 {(3 - x)}^{\frac{1}{3} \cdot 3}}$

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{3 - x} {\sqrt[3]{3 - x}}^{2}}{2 {(3 - x)}^{1}}$

Simplify.

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

Rewrite ${\sqrt[3]{3 - x}}^{2}$ as ${({(3 - x)}^{2})}^{\frac{1}{3}}$ .

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

Simplify the numerator.

Rewrite the expression using the least common index of $6$ .

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

$\frac{{(3 - x)}^{\frac{1}{2}} \sqrt[3]{{(3 - x)}^{2}}}{2 (3 - x)}$

Rewrite ${(3 - x)}^{\frac{1}{2}}$ as ${(3 - x)}^{\frac{3}{6}}$ .

$\frac{{(3 - x)}^{\frac{3}{6}} \sqrt[3]{{(3 - x)}^{2}}}{2 (3 - x)}$

Rewrite ${(3 - x)}^{\frac{3}{6}}$ as $\sqrt[6]{{(3 - x)}^{3}}$ .

$\frac{\sqrt[6]{{(3 - x)}^{3}} \sqrt[3]{{(3 - x)}^{2}}}{2 (3 - x)}$

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

$\frac{\sqrt[6]{{(3 - x)}^{3}} {(3 - x)}^{\frac{2}{3}}}{2 (3 - x)}$

Rewrite ${(3 - x)}^{\frac{2}{3}}$ as ${(3 - x)}^{\frac{4}{6}}$ .

$\frac{\sqrt[6]{{(3 - x)}^{3}} {(3 - x)}^{\frac{4}{6}}}{2 (3 - x)}$

Rewrite ${(3 - x)}^{\frac{4}{6}}$ as $\sqrt[6]{{(3 - x)}^{4}}$ .

$\frac{\sqrt[6]{{(3 - x)}^{3}} \sqrt[6]{{(3 - x)}^{4}}}{2 (3 - x)}$

Combine using the product rule for radicals.

$\frac{\sqrt[6]{{(3 - x)}^{3} {(3 - x)}^{4}}}{2 (3 - x)}$

Multiply ${(3 - x)}^{3}$ by ${(3 - x)}^{4}$ by adding the exponents.

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

$\frac{\sqrt[6]{{(3 - x)}^{3 + 4}}}{2 (3 - x)}$

Add $3$ and $4$ .

$\frac{\sqrt[6]{{(3 - x)}^{7}}}{2 (3 - x)}$

Simplify the numerator.

Factor out ${(3 - x)}^{6}$ .

$\frac{\sqrt[6]{{(3 - x)}^{6} (3 - x)}}{2 (3 - x)}$

Pull terms out from under the radical.

$\frac{(3 - x) \sqrt[6]{3 - x}}{2 (3 - x)}$

Apply the distributive property.

$\frac{3 \sqrt[6]{3 - x} - x \sqrt[6]{3 - x}}{2 (3 - x)}$

Factor $\sqrt[6]{3 - x}$ out of $3 \sqrt[6]{3 - x} - x \sqrt[6]{3 - x}$ .

Factor $\sqrt[6]{3 - x}$ out of $3 \sqrt[6]{3 - x}$ .

$\frac{\sqrt[6]{3 - x} \cdot 3 - x \sqrt[6]{3 - x}}{2 (3 - x)}$

Factor $\sqrt[6]{3 - x}$ out of $- x \sqrt[6]{3 - x}$ .

$\frac{\sqrt[6]{3 - x} \cdot 3 + \sqrt[6]{3 - x} (- x)}{2 (3 - x)}$

Factor $\sqrt[6]{3 - x}$ out of $\sqrt[6]{3 - x} \cdot 3 + \sqrt[6]{3 - x} (- x)$ .

$\frac{\sqrt[6]{3 - x} (3 - x)}{2 (3 - x)}$

Cancel the common factor of $3 - x$ .

Cancel the common factor.

$\frac{\sqrt[6]{3 - x} (3 - x)}{2 (3 - x)}$

Rewrite the expression.

$\frac{\sqrt[6]{3 - x}}{2}$

Simplify (2 square root of 3-x)/(4 cube root of 3-x)

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