More Rational Exponents

line

For each of the following questions, assume all variables are nonnegative real numbers.

1. Multiply x^(1/7)[x^(6/7)+x^(13/7)]


 x2 + x
  x^(7/7)+x^(14/2)
  x^(6/49) + x^(13/49)


2. Multiply (4x^(1/3) - 2)(x^(2/3) + 5)

  4x + 18x^(1/3) - 10
  4x + 20x^(1/3)-2x^(2/3)-10
  4x2 + 18x -10


3. Divide [16x^(8/5) + 24x^(6/5)]/8x^(3/5)

  2x^(11/5) + 3x^(9/5)
  2x+3x^(3/5)
  2x^(5/5)+3x^(3/5)


4. Divide [25x^(5/3)y^(2/3) - 15x^(4/3)y^(1/3)]/[5x^(1/3)y^(1/3)]

 2x^(1/3)y^(1/3)
 5x^2y - 3x^(5/3)y^(2/3)
 5x^(4/3)y^(1/3)-3x



5. Factor 4(x-5)^(3/5)   from   20(x-5)^(4/5) +16(x-5)^(3/5)

 4(x-5)^(3/5)[5(x-5)^(1/5)+16]
 4(x-5)^(3/5)[5(x-5)^(1/5)+4]
 4(x-5)^(3/5)[9(x-5)^(1/5)9]


6. Factor 8(2x+1)^(5/4) from 40(2x+1)^(7/4)+64(2x+1)^(5/4)


 8(2x+1)^(5/4)[5(2x+1)^(1/2)+8]

  8(2x+1)^(5/4)[5(2x+1)^(1/2)+8(2x+1)]
  8(2x+1)^(5/4)[5(2x+1)^(2/4)+16x+8]


7. Simplify  5/x^(4/3) + x^(4/3)into a single fraction


 5x^-(4/3) + 1
  [5 + x^(4/3)]/x^(4/3)
 [5 + x^(8/3)]/x^(4/3)


8. Simplify (6x^3)/(x^2+1)^(1/2) + (x^2+1)^(1/2)


 6x^3(x^2+1)^-(1/2) + 1
  (6x^3 + (x^2+1)^(1/2)) / (x^2 + 1)^1/2
  (6x^3+x^2+1)/(x+1)^(1/2)



line

Copyright © 2001 Donna Tupper.