Expert: Richard J. Raridon - 3/6/2008

Question
Good Morning,
I was hoping you would be able to help me with two problems and check my work on the others.
These two I am struggling with:
Evaluate each numerical expression
((-64)/(27))^ (-1/3)

Simplify expression or perform the indicated operations. Express final result using positive exponents only.
((^3sqrt16) /(^6sqrt4))

Would you mind checking the following answers:
Evaluate each numerical expression
-100^3/2 = -1000
32^ -3/5 = 1/8
(4x + 3y) ^3/7 = ^7sqrt(4x + 3y)^3
-20x^1/6y^5/6 = -20^6sqrtxy^5
Write each expression using positive rational exponents
^5sqrtx^4y^3 = x^4/5 y^ 3/5
-^7sqrt(x-y)^5
Simplify each expression or perform the indicated operations. Express final results using positive exponents only.
(6x ^-1/2)(15x ^1/6) = 90 / x^1/3
(4x^1/5 y^1/3)^3 = 64x^3/5y
((3x^3/4)/(2y^1/2))^4 = ((81x^3)/(16y^2))
((y^2)/(x^-3))^-1/3 = ((x)/(y^2/3))
((96x^3/4)/(12x^1/2))^2 = 64x^1/2
(sqrt2)(^3sqrt2) = ^6sqrt32
((sqrt6)/(^4sqrt6)) = ^4sqrt6
((sqrt25)/(^4sqrt5) = ^4sqrt25
Any help is greatly appreciate! Thanks in advance!

Answer
You used exponents.  A square root is simply ^1/2.
((-64)/(27)^(-1/3) = ((27)/(-64))^1/3 = 3/-4 = -3/4
I assume by ^3sqrt you mean a cube root.  You would write that
(16^1/3)/(4^1/6) = (2^4/3)/(2^1/3) = 2
To be correct, you need to write it -(100^3/2) = -1000
(32^-3/5 = 1/8 okay
(4x+3y)^3/7 means you're taking a 7th root of (4x+3y)^3, not what you had
-20x^1/6y^5/6 = -20(xy^5)^1/6
(x^4y^3)^1/5 = x^4/5y^3/5 okay
(x-y)^5/7
90/x^1/3 is correct
It would be a little clearer if you wrote it (64x^3/5)y
I believe it should be 1/(xy^2/3)
64x^1/2 is correct
(2^1/2)(2^1/3) = 2^5/6 = (32)^1/6
(6^1/2)(6^1/4) = 6^3/4
(25^1/2)(5^1/4) = 5(5^1/4) = 5^5/4