Question

Which of the following shows why 6 1/3 is equivalent to 6–√3?

Answer 1

Answer:

Option (4)

Step-by-step explanation:

We have to prove: $6^{\frac{1}{3} }=\sqrt[3]{6}$

To prove this equation we will take $6^{k}=e^{\frac{1}{3}}$

$6^{k}=\sqrt[3]{6}$

$(6^{k})^3=(\sqrt[3]{6})^3$

$6^{3k}=6^1$

By comparing powers of 6 on both the sides,

3k = 1

k = $\frac{1}{3}$

Therefore, $6^{\frac{1}{3}}=\sqrt[3]{6}$

Hence the equation is true.

Option (4) will be the correct opion.