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

y= 10/3x -18dude above me is wrong smh....

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

clay69

06.01.2022

ANSWER

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

EXPLANATION

We want to find the expression that is equivalent to,

$\frac{ \sqrt{2} }{ \sqrt[3]{2} }$

This is the same as:

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

Use the following property of indices

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

This implies that,

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

Simplify to obtain,

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

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