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.