How do you simplify #root3(4)/root5(8)#?

1 Answer
Apr 8, 2017

Answer:

#root(3)(4)/root(5)(8) = root(15)(2)#

Explanation:

Since we are dealing with positive radicands, we can freely combine the exponents like this:

#root(3)(4)/root(5)(8) = (2^2)^(1/3) / (2^3)^(1/5)#

#color(white)(root(3)(4)/root(5)(8)) = 2^(2/3) / 2^(3/5)#

#color(white)(root(3)(4)/root(5)(8)) = 2^(2/3-3/5)#

#color(white)(root(3)(4)/root(5)(8)) = 2^(10/15-9/15)#

#color(white)(root(3)(4)/root(5)(8)) = 2^(1/15)#

#color(white)(root(3)(4)/root(5)(8)) = root(15)(2)#