Question

Which of the following is equal to the square root of the cube root of 6? 6 to the power of one sixth 6 to the power of one third 6 to the power of two thirds 6 to the power of three halves

Answer 1

Answer:

A. $\sqrt{\sqrt[3]{6}}=6^{\frac{1}{6}}$

Step-by-step explanation:

We have been given a number $\sqrt{\sqrt[3]{6}}$. We are asked go find equivalent to the given number.

Using radical rule $\sqrt[n]{a}=a^{\frac{1}{n}}$, we can rewrite our given number as:

$\sqrt{\sqrt[3]{6}}=(6^{\frac{1}{3}})^{\frac{1}{2}}$

Using exponent rule $(a^{m})^n=a^{m\cdot n}$, we will get:

$(6^{\frac{1}{3}})^{\frac{1}{2}}=6^{\frac{1}{3}\times\frac{1}{2}}$

$6^{\frac{1}{3}\times\frac{1}{2}}=6^{\frac{1}{6}}$

Therefore, option A is the correct choice.

Answer 2

Answer:

6 to the power of one sixth.

Step-by-step explanation:

Cube root of 6 = 6^(1/3)  and the square root of this = [ 6^(1/3) ]^1/2

= 6^(1/3 * 1/2)

= 6^(1/6).