20 Jun Radicals can be also be written as numbers with rational exp
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!
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