Algebra Examples

$\sqrt[5]{z^{16}} \sqrt[25]{z^{2} \cdot 0}$

Step 1

Rewrite $z^{16}$ as ${(z^{3})}^{5} z$ .

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Factor out $z^{15}$ .

$\sqrt[5]{z^{15} z} \sqrt[25]{z^{2} \cdot 0}$

Rewrite $z^{15}$ as ${(z^{3})}^{5}$ .

$\sqrt[5]{{(z^{3})}^{5} z} \sqrt[25]{z^{2} \cdot 0}$

Step 2

Pull terms out from under the radical.

$z^{3} \sqrt[5]{z} \sqrt[25]{z^{2} \cdot 0}$

Step 3

Write the expression using exponents.

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

$z^{3} \sqrt[5]{z} \sqrt[25]{0}$

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

$z^{3} \sqrt[5]{z} \sqrt[25]{0^{25}}$

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

$z^{3} \sqrt[5]{z} \cdot 0$

Step 4

Multiply $z^{3} \sqrt[5]{z} \cdot 0$ .

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Multiply $0$ by $z^{3}$ .

$0 \sqrt[5]{z}$

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

$0$