0.9^18 Updated -

So:

[ 0.9^{18} \approx 0.1500946353 ]

We can compute stepwise:

( 0.9^2 = 0.81 ) ( 0.9^4 = (0.81)^2 = 0.6561 ) ( 0.9^8 = (0.6561)^2 = 0.43046721 ) ( 0.9^{16} = (0.43046721)^2 = 0.1853020188851841 ) 0.9^18

Let’s calculate ( 0.9^{18} ) step-by-step. So: [ 0

First, ( 0.1853020188851841 \times 0.8 = 0.14824161510814728 ) Then, ( 0.1853020188851841 \times 0.01 = 0.001853020188851841 ) Add them: ( 0.14824161510814728 + 0.001853020188851841 ) Sum: ( 0.15009463529699912 ) 0.9^18

( 0.9^{18} = 0.9^{16} \times 0.9^2 ) ( = 0.1853020188851841 \times 0.81 )