Calculus Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Multiply $\frac{1}{\sqrt[3]{x}}$ by $\frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{2}}$ .

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

Step 1.1.2

Combine and simplify the denominator.

Tap for more steps...

Step 1.1.2.1

Multiply $\frac{1}{\sqrt[3]{x}}$ by $\frac{{\sqrt[3]{x}}^{2}}{{\sqrt[3]{x}}^{2}}$ .

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

Step 1.1.2.2

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

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

Step 1.1.2.3

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

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

Step 1.1.2.4

Add $1$ and $2$ .

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

Step 1.1.2.5

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

Tap for more steps...

Step 1.1.2.5.1

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

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

Step 1.1.2.5.2

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

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

Step 1.1.2.5.3

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

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

Step 1.1.2.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.2.5.4.1

Cancel the common factor.

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

Step 1.1.2.5.4.2

Rewrite the expression.

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

Step 1.1.2.5.5

Simplify.

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

Step 1.1.3

Rewrite ${\sqrt[3]{x}}^{2}$ as $\sqrt[3]{x^{2}}$ .

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

Step 1.2

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

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

Step 2

Expand $(\sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x}) (\sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $\sqrt{x} \sqrt{x}$ .

Tap for more steps...

Step 3.1.1.1

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

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

Step 3.1.1.2

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

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

Step 3.1.1.3

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

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

Step 3.1.1.4

Add $1$ and $1$ .

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

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

Step 3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.2.4.1

Cancel the common factor.

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

Step 3.1.2.4.2

Rewrite the expression.

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

Step 3.1.2.5

Simplify.

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

Step 3.1.3

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

Tap for more steps...

Step 3.1.3.1

Combine $\sqrt{x}$ and $\frac{\sqrt[3]{x^{2}}}{x}$ .

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

Step 3.1.3.2

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

Tap for more steps...

Step 3.1.3.2.1

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

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

Step 3.1.3.2.2

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

$x + \frac{x^{\frac{3}{6}} \sqrt[3]{x^{2}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.2.3

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

$x + \frac{\sqrt[6]{x^{3}} \sqrt[3]{x^{2}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.2.4

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

$x + \frac{\sqrt[6]{x^{3}} x^{\frac{2}{3}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.2.5

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

$x + \frac{\sqrt[6]{x^{3}} x^{\frac{4}{6}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.2.6

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

$x + \frac{\sqrt[6]{x^{3}} \sqrt[6]{x^{4}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.3

Combine using the product rule for radicals.

$x + \frac{\sqrt[6]{x^{3} x^{4}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.4

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

Tap for more steps...

Step 3.1.3.4.1

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

$x + \frac{\sqrt[6]{x^{3 + 4}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.3.4.2

Add $3$ and $4$ .

$x + \frac{\sqrt[6]{x^{7}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.4

Simplify the numerator.

Tap for more steps...

Step 3.1.4.1

Factor out $x^{6}$ .

$x + \frac{\sqrt[6]{x^{6} x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.4.2

Pull terms out from under the radical.

$x + \frac{x \sqrt[6]{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.5

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.5.1

Cancel the common factor.

$x + \frac{x \sqrt[6]{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.5.2

Divide $\sqrt[6]{x}$ by $1$ .

$x + \sqrt[6]{x} + \frac{\sqrt[3]{x^{2}}}{x} \sqrt{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6

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

Tap for more steps...

Step 3.1.6.1

Combine $\frac{\sqrt[3]{x^{2}}}{x}$ and $\sqrt{x}$ .

$x + \sqrt[6]{x} + \frac{\sqrt[3]{x^{2}} \sqrt{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2

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

Tap for more steps...

Step 3.1.6.2.1

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

$x + \sqrt[6]{x} + \frac{x^{\frac{2}{3}} \sqrt{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2.2

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

$x + \sqrt[6]{x} + \frac{x^{\frac{4}{6}} \sqrt{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2.3

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

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4}} \sqrt{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2.4

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

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4}} x^{\frac{1}{2}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2.5

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

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4}} x^{\frac{3}{6}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.2.6

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

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4}} \sqrt[6]{x^{3}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.3

Combine using the product rule for radicals.

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4} x^{3}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.4

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

Tap for more steps...

Step 3.1.6.4.1

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

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{4 + 3}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.6.4.2

Add $4$ and $3$ .

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{7}}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.7

Simplify the numerator.

Tap for more steps...

Step 3.1.7.1

Factor out $x^{6}$ .

$x + \sqrt[6]{x} + \frac{\sqrt[6]{x^{6} x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.7.2

Pull terms out from under the radical.

$x + \sqrt[6]{x} + \frac{x \sqrt[6]{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.8

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.1.8.1

Cancel the common factor.

$x + \sqrt[6]{x} + \frac{x \sqrt[6]{x}}{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.8.2

Divide $\sqrt[6]{x}$ by $1$ .

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{\sqrt[3]{x^{2}}}{x} \cdot \frac{\sqrt[3]{x^{2}}}{x}$

Step 3.1.9

Combine.

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{\sqrt[3]{x^{2}} \sqrt[3]{x^{2}}}{x \cdot x}$

Step 3.1.10

Multiply $x$ by $x$ .

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

Step 3.1.11

Simplify the numerator.

Tap for more steps...

Step 3.1.11.1

Raise $\sqrt[3]{x^{2}}$ to the power of $1$ .

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{{\sqrt[3]{x^{2}}}^{1} \sqrt[3]{x^{2}}}{x^{2}}$

Step 3.1.11.2

Raise $\sqrt[3]{x^{2}}$ to the power of $1$ .

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{{\sqrt[3]{x^{2}}}^{1} {\sqrt[3]{x^{2}}}^{1}}{x^{2}}$

Step 3.1.11.3

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

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{{\sqrt[3]{x^{2}}}^{1 + 1}}{x^{2}}$

Step 3.1.11.4

Add $1$ and $1$ .

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

Step 3.1.12

Simplify the numerator.

Tap for more steps...

Step 3.1.12.1

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

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

Step 3.1.12.2

Multiply the exponents in ${(x^{2})}^{2}$ .

Tap for more steps...

Step 3.1.12.2.1

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

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{\sqrt[3]{x^{2 \cdot 2}}}{x^{2}}$

Step 3.1.12.2.2

Multiply $2$ by $2$ .

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

Step 3.1.12.3

Factor out $x^{3}$ .

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

Step 3.1.12.4

Pull terms out from under the radical.

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

Step 3.1.13

Cancel the common factor of $x$ and $x^{2}$ .

Tap for more steps...

Step 3.1.13.1

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

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

Step 3.1.13.2

Cancel the common factors.

Tap for more steps...

Step 3.1.13.2.1

Factor $x$ out of $x^{2}$ .

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

Step 3.1.13.2.2

Cancel the common factor.

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{x \sqrt[3]{x}}{x \cdot x}$

Step 3.1.13.2.3

Rewrite the expression.

$x + \sqrt[6]{x} + \sqrt[6]{x} + \frac{\sqrt[3]{x}}{x}$

Step 3.2

Add $\sqrt[6]{x}$ and $\sqrt[6]{x}$ .

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