Radicals can be also be written as numbers with rational exponents, which allows you to apply the same properties of rational exponents to them.
First, I will state something from the Law of Indices: ##a^(m/n)=root(n)(a^m)=(root(n)(a))^m##
Okay, for example we want to simplify this: ##root(3)(4) * root(6)(4)##
Because of the Law of Indices, we can write these as numbers with rational exponents. (To make it easier for us, let’s write 4 as ##2^2##) ##root(3)(2^2) * root(6)(2^2)## ##=2^(2/3)*2^(2/6)## ##=2^(2/3)*2^(1/3)## (We simplified ##2^(2/6)## to ##2^(1/3)##)
Remember that when multiplying numbers with the same base, you simply add their exponents. In this case, both numbers have the same base (2). ##2^(2/3)*2^(1/3)## ##=2^((2+1)/3)## ##=2^(3/3)## ##=2^(1)## ##=2##
I’m not sure if this is the answer you are looking for, but I hope it helps!
