smart mathematicians i need your help!!.. pls'?

Question

what are the answers on these radicals.. i need a solution pls...
A. Simply each
1. square root of 10 times cube root of 100

2. square root of 6x times fourth root of 36xsquared

3. cube root of 36xcubey divided by square root of the quantity 2x cube

4. cube root of 54xsquared divided by sixth root of 4xto the forth

5. square root of 8x times square root of 27xyto the fifth all over cube root of 6y

Answer 1

1) √10 · ³√100
= 10^(1/2) · 10^(2/3)
= 10^(7/6)

2) (6x)^(1/2) · (36x²)^(1/4)
= (6x)^(1/2) · (6x)²^(1/4)
= (6x)^(1/2) · (6x)^(2/4)
= 6x

...and so on. Change the radicands to rational exponents with common bases, and follow the rules from there. Good luck!

Answer 2

1. square root of 10 = 10^(1/2) and cube root of 100 = 100^(1/3) = 10^(2/3).
If you multiply 10^(1/2) and 10^(2/3) you will get 10^ (1/2 + 2/3) = 10^(7/6) = sixth root of (10^7) or (sixth root of 10)^7

2. the fourth root of 36x^2 = the square root of 6x
The square root of 6x multiplied by the square root of 6x equals 6x.

Can you please specify which terms are being cubed or squared? Is it the entire term or just the last component. For example 27xy^5 or (27xy)^5? In number 3, 36x^3 or (36x)^3??