How do you simplify #(\frac { x ^ { 2} y ^ { - 1} } { 2x ^ { 4} y ^ { 4} } ) ^ { 3}#?

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Answer 1 · 2017-09-25T17:45:08

#1/(8x^6y^5)#

Simplify inside the bracket first.

#((color(blue)(x^2)color(red)(y^-1))/(2color(blue)(x^4)y^4))^3#

#=((1)/(2color(blue)(x^2)y^4color(red)(y^1)))^3#

#= (1/(2x^2y^5))^3#

#=1/(8x^6y^5)#

Laws of indices:

To Divide: subtract indices of like bases: #x^2/x^4 = 1/x^(4-2) = 1/x^2#

#y^-1 = 1/y#

To multiply, add indices of like bases: #y^4 xxy^1 = y^5#

Raising a power to a power, multiply the indices

#(x^2)^3 = x^(2xx3) = x^6#