How do you simplify 5/3rd root of 26^2?

1 Answer
George C.
Oct 9, 2015

#root(5/3)(26^2) = (26^2)^(3/5) = 26^(6/5)#

Explanation:

The #n#th root of a number #a# is #a^(1/n)#

So the #5/3#rd root of a number #a# is #a^(3/5)#

In addtion, if #a > 0# and #b, c != 0#, then #(a^b)^c = a^(bc)#

So:

#root(5/3)(26^2) = (26^2)^(3/5) = 26^(2*3/5) = 26^(6/5)#

This cannot be simplified further since #26# has no fifth power factors.

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