Simplify fourth root of 5x* fourth root of 2x

$\sqrt[4]{5 x} \cdot \sqrt[4]{2 x}$

Combine using the product rule for radicals.

$\sqrt[4]{5 x (2 x)}$

Multiply $2$ by $5$ .

$\sqrt[4]{10 x \cdot x}$

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

$\sqrt[4]{10 (x^{1} x)}$

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

$\sqrt[4]{10 (x^{1} x^{1})}$

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

$\sqrt[4]{10 x^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt[4]{10 x^{2}}$