How do you write $2^(7 / 8)/2^(1/4)$ as a radical?

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Answer 1 · 2016-06-05T09:18:31

$root(8)32$

first do division
$2^(7/8-1/4)$
$2^(5/8)$
then it is equivalent to the radical
$root(8)2^5$
or
$root(8)32$

Answer 2 · 2016-06-05T09:21:05

$2^(5/8) = root(8) 2^5$

Using the law of indices for dividing if the bases are the same, we can simplify the f,raction by subtracting the indices to get

$2^(5/8)$

The law of indices involving fractional indices states

$x^(p/q) = root(q) x^p$

So, $2^(5/8) = root(8) 2^5$

The denominator becomes the root and the numerator becomes the power - it can be inside or outside the root sign.

How do you write 2^(7 / 8)/2^(1/4) 2^(7 / 8)/2^(1/4) as a radical?