Question

What is the value of the expressions below?(-8)^4/3A. 32/3B. 16C. -32/3D. -16

Answer 1

`B.\:16`

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

`\begin{gathered} \left(-8\right)^{(4)/(3)} \\ \\ \left(-1\right)^{(4)/(3)}\cdot \:8^{(4)/(3)} \\ \\ \left(\left(-1\right)^{(1)/(3)}\right)^4\cdot\left(2^3\right)^{(4)/(3)} \\ \\ 1\cdot2^4 \\ \\ 16 \end{gathered}`

Any negative number raised to even exponents yields even numbers. Thus, the answer is 16