7.2

$$
\sqrt{2^{x} \sqrt{4^{x} \cdot 0.125^{\frac{1}{x}}}}=4 \sqrt[3]{2}
$$
7.2 Applying the rule of extracting the root from the power and formulas (1.19) and (1.16), we get

$2^{\frac{x}{2}} \cdot 2^{\frac{x}{3}} \cdot 0.5^{\frac{1}{2 x}}=2^{2} \cdot 2^{\frac{1}{3}}$, or $2^{\frac{x}{2}+\frac{x}{3}-\frac{1}{2 x}}=2^{\frac{7}{3}}$.

According to the hint $1^{0}$, we transition to the equivalent equation $\frac{5 x^{2}-3}{6 x}=\frac{7}{3}$, from which $x_{1}=-\frac{1}{5}, x_{2}=3$.

Answer: $x_{1}=-0.2, x_{2}=3$.