How do you simplify #(\frac { x } { y ^ { 3} } ) ^ { 0} ( \frac { x ^ { 5} } { y ^ { 2} } ) ( x y ^ { 2} ) ^ { 2}#?

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Answer 1 · 2016-11-19T14:13:29

#x^7*y^2#

First, let's work with #(x/y^3)^0#. Anything to the #0# power is 1.

Therefore this question can be rewritten as:

#1*(x^5/y^2)(xy^2)^2 =>#

#(x^5/y^2)(xy^2)^2#

Next, simplify #(xy^2)^2# using the rules for exponents:

#(xy^2)^2 => (x^(1*2)y^(2*2)) => (x^2y^4)#

Then this question can be rewritten as:

#(x^5/y^2)(x^2y^4) =>#

#((x^5)*(x^2y^4))/y^2 =>#

#(x^(5+2)*y^4)/y^2 =>#

#(x^7*y^4)/y^2 =>#

#x^7*y^(4-2) =>#

#x^7*y^2#