How do you simplify #(2^-1 cd^-4) (8c^-3 d^4)#?

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Answer 1 · 2015-06-07T11:51:25

#(2^-1 cd^-4) (8c^-3 d^4)#

#=(2^-1 cd^-4) (2^3c^-3 d^4)#

(#8 = 2^3#)

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

Applying the above to the exponents of #2#, #c# and #d#:

#=color(red)(2^((-1 +3)))color(blue)( c^((1-3))color(green)(d^((-4+4))#

#=color(red)(2^((2)))color(blue)( c^((-2))color(green)(d^((0))#

Note: #color(blue)(a^0 = 1#

#=4.c^(-2).1#
#=4c^-2#