Algebra Examples

$f (x) = \sqrt[4]{\sqrt[5]{\sqrt[2]{x^{17}}}}$

Step 1

Write $f (x) = \sqrt[4]{\sqrt[5]{\sqrt[2]{x^{17}}}}$ as an equation.

$y = \sqrt[4]{\sqrt[5]{\sqrt[2]{x^{17}}}}$

Step 2

Simplify $\sqrt[4]{\sqrt[5]{\sqrt{x^{17}}}}$ .

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Step 2.1

Rewrite $x^{17}$ as ${(x^{8})}^{2} x$ .

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Step 2.1.1

Factor out $x^{16}$ .

$y = \sqrt[4]{\sqrt[5]{\sqrt{x^{16} x}}}$

Step 2.1.2

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$y = \sqrt[4]{\sqrt[5]{\sqrt{{(x^{8})}^{2} x}}}$

Step 2.2

Pull terms out from under the radical.

$y = \sqrt[4]{\sqrt[5]{x^{8} \sqrt{x}}}$

Step 2.3

Rewrite $x^{8} \sqrt{x}$ as $x^{5} (x^{3} \sqrt{x})$ .

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Step 2.3.1

Factor out $x^{5}$ .

$y = \sqrt[4]{\sqrt[5]{x^{5} x^{3} \sqrt{x}}}$

Step 2.3.2

Add parentheses.

$y = \sqrt[4]{\sqrt[5]{x^{5} (x^{3} \sqrt{x})}}$

Step 2.4

Pull terms out from under the radical.

$y = \sqrt[4]{x \sqrt[5]{x^{3} \sqrt{x}}}$