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

2 Answers
Jun 5, 2016

#root(8)32#

Explanation:

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#

Jun 5, 2016

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

Explanation:

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.