(-8)^(4/3) is equals with 16 or (-16)*(-1)^(1/3)? 1. $(-8)^{4/3}=\bigl((-8){^4\bigr)^{1/3}}=4096^{1/3}=16$.
2. 
$$
\begin{align*}
  (-8)^{4/3} &= (-8)^{1+1/3} \\
               &= -8\times(-8)^{1/3} \\
               &= -8\times (-1)^{1/3}\times 8^{1/3} \\
               &= -2\times 8\times (-1)^{1/3} \\
               &= -16\times (-1)^{1/3}.
\end{align*}
$$
So, which is the correct?

Let $a$ be any real number. We can show that the equation
$$
  x^3 = a
$$
has one and only one real root. It is called the cube root of $a$ and
is denoted $a^{1/3}$ or $\sqrt[3]{a}$.
From $(-1)^3 = -1$, we conclude that $(-1)^{1/3} = -1$.
