How do you simplify #\frac { 3x ^ { 2} y ^ { - 2} } { 9x ^ { 4} y ^ { - 5} }#?

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Answer 1 · 2018-01-08T04:37:28

#color(blue)((3x^2 y^-2)/(9x^4y^-5) = y^3/(3x^2))#

Given:

#color(red)((3x^2 y^-2)/(9x^4y^-5)#

Rewrite this rational expression as

#(3/9)(x^2/x^4)(y^-2/y^-5)#

We can use the following formulas to simplify:

#color(blue)(a^m/a^n = a^ (m-n))# and

#color(blue)(a^ (-b) = 1/a^b)#

Now let us look at the expression:

#(3/9)(x^2/x^4)(y^-2/y^-5)#

#rArr (1/3)(x^(2-4))[(y^(-2)-(-5)]#

#rArr (1/3)(x^(-2))(y^(-2+5))#

#rArr (1/3)(x^(-2))(y^(3))#

#rArr (1/3)(1/x^(2))(y^(3)/1)#

#rArr(y^3/(3x^2))#

Hence,

#color(blue)((3x^2 y^-2)/(9x^4y^-5) = y^3/(3x^2))#