[tex]B.\:16[/tex]
1) Let's apply in this case, the property of rational exponents.
2) Thus, let's rewrite it and solve it by distributing the exponent over the product below
[tex]\begin{gathered} \left(-8\right)^{\frac{4}{3}} \\ \\ \left(-1\right)^{\frac{4}{3}}\cdot \:8^{\frac{4}{3}} \\ \\ \left(\left(-1\right)^{\frac{1}{3}}\right)^4\cdot\left(2^3\right)^{\frac{4}{3}} \\ \\ 1\cdot2^4 \\ \\ 16 \end{gathered}[/tex]
Any negative number raised to even exponents yields even numbers. Thus, the answer is 16
