# Math Help - Does this Make sense?

1. ## Does this Make sense?

Could someone try to explain if it does? Thank you

2. Try using powers in parentheses. This expression is equivalent to

$((a/b) \cdot x)^{1/2}$

where
$x = ((b/a) \cdot (a/b)^{1/2})^{1/2}$.

Let's evaluate x.
$x = ((a/b)^{-1} \cdot (a/b)^{1/2})^{1/2}$

$x = ((a/b)^{-1/2})^{1/2}$

$x = (a/b)^{-1/4}$

Now for the original expression:
$((a/b) \cdot (a/b)^{-1/4})^{1/2}$
$((a/b)^{3/4})^{1/2}$
$(a/b)^{3/8}$

Hence k = 3/8.