Algebra Examples

$\sqrt[5]{x^{11}} \sqrt[25]{x^{2} \cdot 0}$

Step 1

Rewrite $x^{11}$ as ${(x^{2})}^{5} x$ .

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Step 1.1

Factor out $x^{10}$ .

$\sqrt[5]{x^{10} x} \sqrt[25]{x^{2} \cdot 0}$

Step 1.2

Rewrite $x^{10}$ as ${(x^{2})}^{5}$ .

$\sqrt[5]{{(x^{2})}^{5} x} \sqrt[25]{x^{2} \cdot 0}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt[5]{x} \sqrt[25]{x^{2} \cdot 0}$

Step 3

Write the expression using exponents.

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Step 3.1

Multiply $x^{2}$ by $0$ .

$x^{2} \sqrt[5]{x} \sqrt[25]{0}$

Step 3.2

Rewrite $0$ as $0^{25}$ .

$x^{2} \sqrt[5]{x} \sqrt[25]{0^{25}}$

Step 3.3

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

$x^{2} \sqrt[5]{x} \cdot 0$

Step 4

Multiply $x^{2} \sqrt[5]{x} \cdot 0$ .

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Step 4.1

Multiply $0$ by $x^{2}$ .

$0 \sqrt[5]{x}$

Step 4.2

Multiply $0$ by $\sqrt[5]{x}$ .

$0$