A6 The exact value of the expression $\sqrt[6]{0.125^{-0.6}}$ is:
(A) $\sqrt[3]{2}$
(B) $\sqrt{2}$
(C) $\sqrt[3]{5}$
(D) $\sqrt[6]{2}$
(E) $\sqrt[6]{5}$

## II. PART
A6. The periodic decimal number $0, \overline{6}=\frac{6}{9}=\frac{2}{3}$. The decimal number 0.125 can be written as the fraction $\frac{1}{8}$. Thus, the expression $\sqrt[6]{0.125^{-0, \overline{6}}}$ can be written as $\left(\left(\frac{1}{8}\right)^{-\frac{2}{3}}\right)^{\frac{1}{6}}$. The fraction $\frac{1}{8}$ can be written as a power and we consider the negative exponent. We get $\left(\left(2^{3}\right)^{\frac{2}{3}}\right)^{\frac{1}{6}}$, multiply the exponents or simplify them appropriately, and we get $2^{\frac{1}{3}}$, which is $\sqrt[3]{2}$.

## Group B