How do you simplify #( 3c^ -4 d^5)^2 * 12cd^ -4#?

1 Answer
Oct 1, 2015

Answer:

#= color(blue)(108 c^(-7) d ^(6)#

Explanation:

#(3c^-4d^5)^color(blue)(2)⋅12cd^-4#

  • As per property :
    #color(blue)((a^m))^n= a^(color(blue)(mn#

Applying the above to the first term:
#= (3^color(blue)(2) * c^color(blue)(-4*2) * d ^color(blue)(5*2))⋅12cd^-4#

#= 9c^color(blue)(-8) d ^color(blue)(10 )⋅12cd^-4#

  • As per property:
    #color(blue)(a^m*a^n=a^(m+n)#
    Applying the same to exponents of #c# and #d#

#= (9 * 12 ) * c^(-8) * c^1* d ^10 *d^-4#

#= 108 * c^(-8+1) * d ^(10-4)#

#= color(blue)(108 c^(-7) d ^(6)#