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How do you simplify #(4p^2)^8 / (4p^2)^6 #?

1 Answer

Mar 24, 2016

#= 16 p^ (4)#

Explanation:

#((4p^2)^8) / ((4p^2)^6)#

By property:
#color(blue)((a^m))^n = a ^(mn)#

#((4p^2)^8) / ((4p^2)^6)= ((4^8p^(2 * 8 ) )) / ((4^ 6 p^( 2 * 6))#

#= ((4^8p^ 16 )) / ((4^ 6 p^12)#

#= (4^8 / 4 ^6) * (( p^ 16 )) / ((p^12)#

By property:
#color(blue)(a^m / a ^n = a ^(m-n)#

#= 4^((8 - 6 ) * ( p^ (16 -12 ))#

#= 4^(2 ) p^ (4)#

#= 16 p^ (4)#

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