How do you evaluate #8^3*12^2*1/3^4#?

1 Answer
George C.
May 2, 2016

#8^3*12^2*1/(3^4)=8192/9= 910.bar(2)#

Explanation:

#8^3*12^2*1/(3^4)#

#=((2^3)^3*(2^2*3)^2)/(3^4)#

#=(2^9*2^4*color(red)(cancel(color(black)(3^2))))/(3^2*color(red)(cancel(color(black)(3^2))))#

#=(2^13)/(3^2)#

#=8192/9#

#= 910 2/9#

#= 910.bar(2)#

#color(white)()#
Alternatively:

#8^3*12^2*1/(3^4)#

#=((8*8*8)*(12*12))/(3*3*3*3)#

#=(512*144)/81#

#=(512*16*color(red)(cancel(color(black)(9))))/(9*color(red)(cancel(color(black)(9))))#

#=8192/9#

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