Question

Which expression is equivalent

Answer 1

Answer:

$\sqrt[6]{2\\}$

Step-by-step explanation:

Rewriting

2 ^1/2 ÷ 2 ^ 1/3

We know a^ b ÷ a^c = a^ (b-c)

2 ^ (1/2 -1/3)

Getting a common denominator

2^ ( 3/6 - 2/6)

2^ 1/6

$\sqrt[6]{2\\}$

Answer 2

Answer:

$\sqrt[6]{2}$

Step-by-step explanation:

We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and $2^{\frac{1}{2} }$ and the cube root of two is the same as $2^{\frac{1}{3} }$. Therefore, we can rewrite the expression:

$\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}$

Now, to write them as one power of two, we can use the quotient rule which states, $\frac{x^m}{x^n} = x^{m-n}$:

$2^{\frac{1}{2} -\frac{1}{3}}$

We just need to subtract 1/3 from 1/2 to get:

$2^{\frac{1}{6} }$

This is the same as the 6th root of 2, which is the second option.