Simplify sixth root of 7* sixth root of 7^5

$\sqrt[6]{7} \cdot \sqrt[6]{7^{5}}$

Combine using the product rule for radicals.

$\sqrt[6]{7 \cdot 7^{5}}$

Multiply $7$ by $7^{5}$ by adding the exponents.

Multiply $7$ by $7^{5}$ .

Raise $7$ to the power of $1$ .

$\sqrt[6]{7^{1} \cdot 7^{5}}$

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

$\sqrt[6]{7^{1 + 5}}$

Add $1$ and $5$ .

$\sqrt[6]{7^{6}}$

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

$7$