Question

Which expression is equivalent to √2/^3√2

Answer 1

6√2

Explanation:

Just did it

Answer 2

`{2}^{ (1)/(6) }`

EXPLANATION

We want to find the expression that is equivalent to,

`\frac{ √(2) }{ \sqrt[3]{2} }`

This is the same as:

`\frac{ {2}^{ (1)/(2) } }{ {2}^{ (1)/(3) } }`

Use the following property of indices

`\frac{ {a}^(m) }{ {a}^(n) } = {a}^(m - n)`

This implies that,

`\frac{ {2}^{ (1)/(2) } }{ {2}^{ (1)/(3) } } = {2}^{ (1)/(2) - (1)/(3) }`

Simplify to obtain,

`{2}^{ (3 - 2)/(6) } = {2}^{ (1)/(6) }`