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 nth root of a number a is a^(1/n)

So the 5/3rd 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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