How do you simplify #x^-4/(2xy^3*(2x^3y^2)^3)#?

1 Answer
Jan 11, 2017

Answer:

#1/(16x^14y^9)#

Explanation:

Before we start note that #2# is the same as #2^1#

#color(blue)("Consider "x^(-4))#

#x^(-4)# is the same as #1/x^4#

As an additional point: #1/x^(-4)# is the same as #x^4#
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#color(blue)("Consider "(2x^3y^2)^3#

This is the same as #(2x^3y^2)xx(2x^3y^2)xx(2x^3y^2)#

Giving:#" "8x^9y^6#

So as a general case:#" "(x^ay^b)^c = x^(axxc)y^(bxxc)#
So for #(2x^3y^2)^3 = 2^(1xx3)x^(3xx3)y^(2xx3)#

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#color(blue)("Putting it all together")#
#x^-4/(2xy^3(2x^3y^2)^3) = 1/x^4xx 1/(2xy^3(2x^3y^2)^3)=1/x^4xx1/(2xy^3xx8x^9y^6)#

#" "=1/(16x^14y^9)#