How do you simplify root3(4)/root5(8)?
1 Answer
Apr 8, 2017
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)
