How do you simplify #(x ^ { - 1} y ^ { 2} \cdot 2y x ^ { 2} ) ^ { - 4}#?

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Answer 1 · 2016-12-08T02:20:27

#2^-4x^-4y^-12# or #1/(16x^4y^12)#

First, combine the terms within the parenthesis using the rules for exponents, particularly: #color(red)(x^a*x^b = x^(a+b))#:

#(2x^(-1+2)y^(2+1))^-4#

#(2x^1y^3)^-4#

Next, simplify the term in parenthesis again using the rules for exponents, this time: #color(red)(((x^a)^b = x^(a*b))#:

#2^-4x^(1*-4)y^(3*-4)#

#2^-4x^-4y^-12#

Or using another rule for exponents, namely #color(red)(x^a = 1/x^-a)#:

#1/(2^4x^4y^12)#

#1/(16x^4y^12)#