Basic Math Examples

${(\sqrt[10]{5})}^{14}$

Step 1

Rewrite ${\sqrt[10]{5}}^{14}$ as $\sqrt[10]{5^{14}}$ .

$\sqrt[10]{5^{14}}$

Step 2

Raise $5$ to the power of $14$ .

$\sqrt[10]{6103515625}$

Step 3

Rewrite $6103515625$ as $5^{10} \cdot 625$ .

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Step 3.1

Factor $9765625$ out of $6103515625$ .

$\sqrt[10]{9765625 (625)}$

Step 3.2

Rewrite $9765625$ as $5^{10}$ .

$\sqrt[10]{5^{10} \cdot 625}$

Step 4

Pull terms out from under the radical.

$5 \sqrt[10]{625}$

Step 5

Rewrite $625$ as $25^{2}$ .

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

Step 6

Rewrite $\sqrt[10]{25^{2}}$ as $\sqrt[5]{\sqrt{25^{2}}}$ .

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

Step 7

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

$5 \sqrt[5]{25}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[5]{25}$

Decimal Form:

$9.51826969 \dots$