Fractional exponents, radicals

What expressions, 1 through 5?

for 1st quest it is sqrt of 36
which is 6

for 2nd question it is 27^-4/3  = (3^3)^-4/3 = 3^-4 = 1/81

for 3rd question...it is not a real number because even root of a negative number is imaginary number and not a real number.

for 4th question 81^1/4 = (3^4)^1/4 = 3

for 5th question 4x^2 multiply y^1/2 divided by x^4 multiply 7y^3
{4x^2} * {y^1/2} / {x^4} * 7y^3
taking exponents and constant terms together
4*7 = 28
x^2 * x^4= x^6
y^3/y^1/2 = y^(3-1/2) = y^(5/2)
so final answer is 28*x^6*y^5/2     * means multiplied by

1) 36 ^ 1/2 means the square root of 36 which is + or - 6
2) 27 ^ -4/3 means the cube root of 27 to the -4th power which is 1/81
3) -10000 ^ 1/4 means the fourth root of -10000 which will not be a real number because you cant have a negative inside an even root (root of 2, 4, 6, 8...)
4) 81 ^ 1/4 root means fourth root of 81 which can be + or - 3

1) 36 ^ 1/2 is the square root of 36, which is 6.
2) 27 to the - 4/3 can be thought of as the the cube root of 27 raised to the -4 power. This is 3 ^ -4, which can be thought of as 3^4 raised to the -1 power. This is 81^-1, which is 1/81.
3) Any number squared will be a positive number, so taking the root of a negative number will return an imaginary number. This is not a real number.
4) Similar to #2, this is a reversal of 3^4. Thus the answer is 3.
5)Take 4x^2 and divide by x^4 to get 4x^-2. Add the exponents of the y terms together to get 7y^7/2. Together, this is 28x^-2y^7/2

1)   6

2)   not a real number

3)    -10

4)      3

5)     4x²?y
         ×  7y³
           x?

Thank you, that is very helpful.