How do you simplify #(3x^7y^3)^4/(12xy^3)#?

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Answer 1 · 2015-06-12T16:56:01

# color(blue)(27/4x^27.y^9#

#(3x^7y^3)^4/(12xy^3)#

#(3x^7y^3)^color(red)(4) = 3^color(red)(4).x^(7 . color(red)(4)). y^(3 .color(red)(4)#

# = 3^4x^28y^12#

now the expression can be re written as :
# (3^4x^28y^12)/(12xy^3)#

Note :
#color(blue)(a^m . a^n = a^(m+n)#
#color(blue)(a^m/a^ n=a^(m-n)#

Applying the above to the exponents of #x# and #y#

#= (81/12) . x^(28-1) . y^(12-3#
# = color(blue)(27/4x^27.y^9#