Algebra Examples

$\sqrt[32]{x \cdot x^{2} \cdot x^{5}}$

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

$\sqrt[32]{x^{1} \cdot x^{2} x^{5}}$

Step 1.1.2

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

$\sqrt[32]{x^{1 + 2} x^{5}}$

Step 1.2

Add $1$ and $2$ .

$\sqrt[32]{x^{3} x^{5}}$

Step 2

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

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Step 2.1

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

$\sqrt[32]{x^{3 + 5}}$

Step 2.2

Add $3$ and $5$ .

$\sqrt[32]{x^{8}}$

Step 3

Rewrite $\sqrt[32]{x^{8}}$ as $\sqrt[4]{\sqrt[8]{x^{8}}}$ .

$\sqrt[4]{\sqrt[8]{x^{8}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[4]{x}$