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

Question

asked Oct 5, 2020 125k views

2 Answers

Mr Hyde · Answer 1 · 2020-10-10T14:19:52+0000

ANSWER

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

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,

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