Multiplying Radicals

I like to convert to exponential form  and work with that

We can convert back to radical form at the last

Note that  ∛  =  exponent (1/3)

( 15x)^(1/3) *  (9x^3)^(1/3)  =

( 145 x^4)^(1/3)

Note  ......(145)^(1/3)  =  (5 * 3^3 )^(1/3)  =  5^(1/3) * (3^3)^(1/3)  =

5^(1/3)  *  3        (1)

Also.....note how to simplify  ( x^4)^(1/3)  =  x^(4/3)

Make  4/3  a mixed number  =  1 + 1/3

So  we have  x^(1 + 1/3)  = x^(1) * (x)^(1/3)   =  x * (x)^(1/3)   (2)

So...putting (1)  and (2) together, we have

3 * x *  (5)^(1/3) * (x)^)1/3)  =

3x ∛ [ 5 x ] 

(4r^3)^(1/3)  *  (5r^3)^(1/3)  = 

[ 4 * 5] ^(1/3) *  [ r^3 * r^3 ]^(1/3)  = 

[ 20 r^6 ] ^(1/3)  =

[20]^(1/3)  *  (r^6)^(1/3)  =

20^(1/3) *  r^2  =

r^2 ∛ 20