Yeah I know.....we are using a lot of exponential rules here
Here are a few that I employed
m √ [ a^n ] converts to exponential form (a)^(n/m)
And
a^(m) * a^(n) = a^(m + n)
And
Remember.... we can take something out of a radical when we have (a)^(n/m) and n ≥ m
For instance...let's suppose that we have 3 √ [ 4^5]
In exponential form....we have (4)^(5/3)
To determine how many powers of 4 come out of the radical and how many stay in.....write the exponent as a mixed number
4^(1 +2/3)
The whole number tells us that 1 power of 4 comes out of the radical and the numerator of the fraction tells us that 2 powers of 4 stay inside the radical...so we have
4 3√ [4^2 ] = 4 3√ [ 16 ]
But note that 16 = 2^4....so...we can apply this rule once more
We have 4 3√ [2^4 ] = 4 (2)^(4/3)
To determine how many powers of 2 that we can take out of the radical and how many we can leave in...write this as
4 (2)^(1 + 1/3)....so....we can take 1 power of 2 out of the radical and 1 power of 2 stays in
So..putting this all together, we have
(4 * 2) 3√2 = 8 3√2
Hang in there, RP......you will begin to understand this
