Simplify the Radical Expression fourth root of 10^5* fourth root of 10

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

Combine using the product rule for radicals.

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

Raise $10$ to the power of $5$ .

$\sqrt[4]{100000 \cdot 10}$

Multiply $100000$ by $10$ .

$\sqrt[4]{1000000}$

Rewrite $1000000$ as $10^{4} \cdot 100$ .

Factor $10000$ out of $1000000$ .

$\sqrt[4]{10000 (100)}$

Rewrite $10000$ as $10^{4}$ .

$\sqrt[4]{10^{4} \cdot 100}$

Pull terms out from under the radical.

$| 10 | \sqrt[4]{100}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$10 \sqrt[4]{100}$

Rewrite $100$ as $10^{2}$ .

$10 \sqrt[4]{10^{2}}$

Rewrite $\sqrt[4]{10^{2}}$ as $\sqrt{\sqrt{10^{2}}}$ .

$10 \sqrt{\sqrt{10^{2}}}$

Pull terms out from under the radical.

$10 \sqrt{| 10 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$10 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{10}$

Decimal Form:

$31.62277660 \dots$