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Simplify (10 root of 5)^14

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

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

$5^{10} \cdot 625$ .

Factor

$9765625$ out of

$6103515625$ .

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

Rewrite

$9765625$ as

$5^{10}$ .

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

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

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:

$9.51826969 \dots$

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