Simplify sixth root of 6^5* sixth root of 6

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

Combine using the product rule for radicals.

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

Multiply $6^{5}$ by $6$ by adding the exponents.

Multiply $6^{5}$ by $6$ .

Raise $6$ to the power of $1$ .

$\sqrt[6]{6^{5} \cdot 6^{1}}$

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

$\sqrt[6]{6^{5 + 1}}$

Add $5$ and $1$ .

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

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

$6$