Simplify the expression

Question

Simplify the expression (x^3 y^4 z^4 x^-3/x^5 y^3 z^5 y^4)^-2   into the form x^r y^s z^t and identify r,s, and t.

 

r=

s=

t=

Answer 1

(x^3y^4z^4x^-3/x^5y^3z^5y^4)^-2 = (y^4z^4/x^5y^3z^5y^4)^-2  (in this step, x^3 and x^-3 cancel out in the numerator, that is, x^3x^-3 = x^3-3 = x^0 = 1).

 

Next, above expression further simplifies to:  (x^-5y^-3z^-1)^-2  (this is just by bringing denominator quantities to numerator; when you do this, signs change, like, x^5 in denominator will become x^-5 in numerator, etc.

 

Then, when we raise everything in numerator in the above expression by power of -2, the result is simply:

 

                                                                  x^10y^6z^2   Therefore, r=10, s=6, t=2