Algebra Examples

$f (x) = x \sqrt[3]{x^{2} \cdot x^{5} \cdot \sqrt[6]{x \sqrt{x}}}$

Step 1

Write $f (x) = x \sqrt[3]{x^{2} \cdot x^{5} \cdot \sqrt[6]{x \sqrt{x}}}$ as an equation.

$y = x \sqrt[3]{x^{2} \cdot x^{5} \cdot \sqrt[6]{x \sqrt{x}}}$

Step 2

Simplify $x \sqrt[3]{x^{2} \cdot x^{5} \cdot \sqrt[6]{x \sqrt{x}}}$ .

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Step 2.1

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

$y = x \sqrt[3]{x^{2 + 5} \sqrt[6]{x \sqrt{x}}}$

Step 2.2

Add $2$ and $5$ .

$y = x \sqrt[3]{x^{7} \sqrt[6]{x \sqrt{x}}}$

Step 2.3

Rewrite $x^{7} \sqrt[6]{x \sqrt{x}}$ as ${(x^{2})}^{3} (x \sqrt[6]{x \sqrt{x}})$ .

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Step 2.3.1

Factor out $x^{6}$ .

$y = x \sqrt[3]{x^{6} x \sqrt[6]{x \sqrt{x}}}$

Step 2.3.2

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$y = x \sqrt[3]{{(x^{2})}^{3} x \sqrt[6]{x \sqrt{x}}}$

Step 2.3.3

Add parentheses.

$y = x \sqrt[3]{{(x^{2})}^{3} (x \sqrt[6]{x \sqrt{x}})}$

Step 2.4

Pull terms out from under the radical.

$y = x (x^{2} \sqrt[3]{x \sqrt[6]{x \sqrt{x}}})$

Step 2.5

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.5.1

Move $x^{2}$ .

$y = x^{2} x \sqrt[3]{x \sqrt[6]{x \sqrt{x}}}$

Step 2.5.2

Multiply $x^{2}$ by $x$ .

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Step 2.5.2.1

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

$y = x^{2} x^{1} \sqrt[3]{x \sqrt[6]{x \sqrt{x}}}$

Step 2.5.2.2

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

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

Step 2.5.3

Add $2$ and $1$ .

$y = x^{3} \sqrt[3]{x \sqrt[6]{x \sqrt{x}}}$