How do you simplify #3x²y * (4x^5 y)^-2#?

1 Answer
Jun 8, 2015

#(3x^²y) * (4x^5 y)^color(red)(-2#
#=(3x²y) * (4^color(red)(-2) . x^(5 . color(red)((-2))). y^color(red)(-2))#
#=(3x²y) * (4^-2 x^(-10)y^(-2))#

note: #color(blue)(a^m.a^n = a^(m+n)#

Applying the above property to the exponents of #color(blue)(x and y#

#=(3.4^-2) . color(blue)(x^(2+(-10)) . y^(1+(-2))#
#=(3.4^-2) . color(blue)(x^-8 . y^-1#

note: #color(blue)(4^-2 = 1/4^2 = 1/16#

#=color(blue)(3/16x^-8y^(-1)#