Question

Which of the following shows the correct steps to find the value of 8 to the power of 1/3?

Answer 1

`8^{(1)/(3)}=(2^3)^{(1)/(3)}=(2)^{3((1)/(3))}=2\text{ (option B)}`

Step-by-step explanation:

`\begin{gathered} 8\text{ to the power of 1/3 = }8^{(1)/(3)} \\ 8=2^3 \end{gathered}`
`\begin{gathered} 8^{(1)/(3)}=(2^3)^{(1)/(3)} \\ =(2^3)^{(1)/(3)}=(2)^{3((1)/(3))} \end{gathered}`
`\begin{gathered} =(2)^{3((1)/(3))}=(2)^{(3)/(3)} \\ =2^1 \\ =\text{ 2} \\ \text{the correct option:} \\ 8^{(1)/(3)}=(2^3)^{(1)/(3)}=(2)^{3((1)/(3))}=2\text{ (option B)} \end{gathered}`