Question

Is this correct

cube root 3√540r^3 s^2 t^9

cube root 3√4(5)(3)(3)(3)r^3s^2 (T^3)^3
3r^t^3 cube root 3√4(5)s^2

3r^t^3 cube root 3√20s^2

Answer 1

is this the answer
3rt cube root 3√20s^2

Answer 2

Without brackets, your question and your answer is ambigious.

I will assume you want
cuberoot(3√540 r^3 s^2 t^9)

= (3√540r^3 r^3 s^2 t^9)^(1/3)
= [3√((36)(15) r^3 s^2 (t^3)^3]^(1/3)
= [ 18√15 r^3 s^2 (t^3)^3]^(1/3)
= (18√15)^(1/3) r s^(2/3) t^3
according to my interpretation of your question

Answer 3

Seems we want cube roots:

∛540r^3 s^2 t^9
= ∛27*20 r^3 s^2 (t^3)^3
= 3rt^3 ∛20s^2

so, yes, you are correct