Question

Question #68395

Answer 1

Radicals can be also be written as numbers with rational exponents, which allows you to apply the same properties of rational exponents to them.

Explanation:

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!