Simplify sixth root of 3^5* sixth root of 3^5

$\sqrt[6]{3^{5}} \cdot \sqrt[6]{3^{5}}$

Combine using the product rule for radicals.

$\sqrt[6]{3^{5} \cdot 3^{5}}$

Multiply $3^{5}$ by $3^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{3^{5 + 5}}$

Add $5$ and $5$ .

$\sqrt[6]{3^{10}}$

Raise $3$ to the power of $10$ .

$\sqrt[6]{59049}$

Rewrite $59049$ as $3^{6} \cdot 81$ .

Factor $729$ out of $59049$ .

$\sqrt[6]{729 (81)}$

Rewrite $729$ as $3^{6}$ .

$\sqrt[6]{3^{6} \cdot 81}$

Pull terms out from under the radical.

$3 \sqrt[6]{81}$

Rewrite $81$ as $9^{2}$ .

$3 \sqrt[6]{9^{2}}$

Rewrite $\sqrt[6]{9^{2}}$ as $\sqrt[3]{\sqrt{9^{2}}}$ .

$3 \sqrt[3]{\sqrt{9^{2}}}$

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

$3 \sqrt[3]{9}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{9}$

Decimal Form:

$6.24025146 \dots$