Trigonometry Examples

$\sqrt[4]{x - \sqrt[6]{x}} + \sqrt[3]{x}$

Step 1

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

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

Step 2

Factor $x^{\frac{1}{6}}$ out of $x - x^{\frac{1}{6}}$ .

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Step 2.1

Raise $x$ to the power of $1$ .

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

Step 2.2

Factor $x^{\frac{1}{6}}$ out of $x^{1}$ .

$\sqrt[4]{x^{\frac{1}{6}} x^{\frac{5}{6}} - x^{\frac{1}{6}}} + \sqrt[3]{x}$

Step 2.3

Factor $x^{\frac{1}{6}}$ out of $- x^{\frac{1}{6}}$ .

$\sqrt[4]{x^{\frac{1}{6}} x^{\frac{5}{6}} + x^{\frac{1}{6}} \cdot - 1} + \sqrt[3]{x}$

Step 2.4

Factor $x^{\frac{1}{6}}$ out of $x^{\frac{1}{6}} x^{\frac{5}{6}} + x^{\frac{1}{6}} \cdot - 1$ .

$\sqrt[4]{x^{\frac{1}{6}} (x^{\frac{5}{6}} - 1)} + \sqrt[3]{x}$