Expert: Sherman D. - 3/10/2004

Question
Here is the next batch of problums I need to study for, please show work and answers, thanks, ^ before a number means that number is an exponent, and numbers between two ~ marks mean they are in a radical, thanks

evaluate expression

1. 16^3/4

2. 25^-3/2

3. -32^4/5

4. (-8)^2/3

write the expression in simpelest form

7. 1/3-1/5

8. 3~3~times~9~

9. 3~8/3~

10. 2^2/3+3(2^2/3)

write the expression in simplest form, assume all variables are positive

11. 3~x^2~times~x~

12. (x^2/3)3/4

13. 3~81x5y^3

14. x2/3y
  _________
   x^-2y^3/4

there will likley be one more set of problums tomarrow, but anyway thanks so much for your time.

Answer
If by these you mean

1.)
16^(3/4) = 4thrt(16^3) = 4thrt(4096) = ±8
or
(16^3)/4 = (4096)/4 = 1024

2.)
25^(-3/2) = 1/(25^(3/2)) =
1/(sqrt(25^3)) = 1/(sqrt(15625)) = ±1/125  

3.)
-32^(4/5) = 5thrt(-(32)^4) = 5thrt(1048576) = -16

4.)
(-8)^2/3 = cbrt((-8)^2) = cbrt(64) = 4

write the expression in simpelest form

7.)
(1/3) - (1/5) = (5/15) - (3/15) = 2/15

8.)
cbrt(3) * sqrt(9) = cbrt(3) * ±3 = ±3cbrt(3)

9.)
cbrt(8/3) = (8/3)^(1/3) = (8^(1/3))/(3^(1/3)) = 2/(3^(1/3))
Multiply top and bottom by 3^(2/3)
(2 * 3^(2/3))/3

10.)
2^(2/3) + 3(2^(2/3))
(1 + 3)(2^(2/3))
4(2^(2/3))
4(cbrt(2^2))
4cbrt(4)

write the expression in simplest form, assume all variables are positive

11.)
cbrt(x^2) * sqrt(x)
same as
x^(2/3) * x^(1/2) = x^((2/3) + (1/2)) =
x^((4/6) + (3/6) = x^(7/6)

12.)
(x^(2/3))^(3/4) = x^((2/3) * (3/4)) = x^(6/12) = x^(1/2)

13.)
cbrt(81x^5 * y^3) = cbrt(81) * cbrt(x^5) * cbrt(y^3) =
cbrt(27 * 3) * cbrt(x^3 * x^2) * cbrt(y^3) =
3xycbrt(3x^2)

14.)
(x^(2/3) * y)/(x^-2 * y^(3/4))
x^((2/3) - (-2)) * y^(1 - (3/4))
x^((2/3) + 2) * y^((4/4) - (3/4))
x^((2/3) + (6/3)) * y^(1/4)
x^(8/3) * y^(1/4)

If you meant anything different, please let me know.