Algebra Examples

$\sqrt[10]{x^{5} \cdot x^{4} \cdot x^{2}}$

Step 1

Multiply $x^{5}$ by $x^{4}$ by adding the exponents.

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Step 1.1

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

$\sqrt[10]{x^{5 + 4} x^{2}}$

Step 1.2

Add $5$ and $4$ .

$\sqrt[10]{x^{9} x^{2}}$

Step 2

Multiply $x^{9}$ by $x^{2}$ 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.

$\sqrt[10]{x^{9 + 2}}$

Step 2.2

Add $9$ and $2$ .

$\sqrt[10]{x^{11}}$

Step 3

Factor out $x^{10}$ .

$\sqrt[10]{x^{10} x}$

Step 4

Pull terms out from under the radical.

$x \sqrt[10]{x}$