SOLUTION: Simplify:A) (9x(^-1/2)-x(^1/2))^2 B) x(^-2)y(3(x^-1)y^3)^4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Simplify:A) (9x(^-1/2)-x(^1/2))^2 B) x(^-2)y(3(x^-1)y^3)^4       Log On


   

Question 126466: Simplify:A) (9x(^-1/2)-x(^1/2))^2
B) x(^-2)y(3(x^-1)y^3)^4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
In order to simplify these expressions, you need to recall some of the Rules of Exponents:
When you see a fractional+power expression,
you can convert it to a radical; here you have %28x%5E-1%2F2%29 which will be equal to sqrt%28x%29.

Or, if you have a negative exponent like +%28x%5E-1%29, you can convert it to %281%2Fx%29.
Or, if you have %28x%5Em%29%5En, it will be x%5E%28m%2An%29, and x%5Em%2Ax%5En will be x%5E%28m%2Bn%29



A)
%289x%5E%28-1%2F2%29%29-%28x%5E%281%2F2%29%29%5E2
%28sqrt%289x%29%29-%28sqrt%28x%29%29%5E2

9x+-2%28sqrt%289x%5E2%29%29+%2B+x

9x+-2%283x%29+%2B+x
9x+-6x+%2B+x
10x+-6x
4x

B)

%28x%5E-2%29y%283+%28x%5E-1%29+y%5E3%29%5E4

%281%2Fx%5E2%29y%283+%281%2Fx%29+y%5E3%29%5E4

%281%2Fx%5E2%29y%283%2A+y%5E3+%2Fx%29%5E4
%281%2Fx%5E2%29y%283%5E4+%28y%5E3%29%5E4+%2Fx%5E4%29
%281%2Fx%5E2%29y%2881+%28y%5E12%29+%2Fx%5E4%29
%281%2Fx%5E2%29%2881+%28y%5E13%29+%2Fx%5E4%29
81+%28y%5E13%29+%2F+%28x%5E2%2Ax%5E4%29
81+y%5E13%2F+x%5E6