Question

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

Answer 1

`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`