Question

MAN IF U ANSWER THIS QUESTION U ENDED 2020 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

A) 6^1/6 or 6 to the power of 1 sixth

Answer 2

6 to the power of 1/6

Explanation:

In general, a root is the same as a fractional power. That is, ...

`\sqrt[n]{x}=x^{(1)/(n)}`

So, the square root of a cube root is ...

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

According to the rules of exponents, a power of a power is ...

(a^b)^c = a^(bc)

so, the above root of a root is ...

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

The square root of the cube root of 6 is 6 to the power of 1/6.