Simplify the following:
(3^2×2^3)/3^3+3/3^3
Combine powers. (3^2×2^3)/3^3 = 3^(2-3)×2^3:
3^2-3×2^3+3/3^3
2-3 = -1:
3^-1×2^3+3/3^3
Combine powers. 3/3^3 = 3^(1-3):
2^3/3+3^1-3
1-3 = -2:
2^3/3+3^-2
2^3 = 2×2^2:
2×2^2/3+3^(-2)
2^2 = 4:
(2×4)/3+3^(-2)
2×4 = 8:
8/3+3^(-2)
3^(-2) = 1/9:
8/3+1/9
Put 8/3+1/9 over the common denominator 9. 8/3+1/9 = (3×8)/9+1/9:
(3×8)/9+1/9
3×8 = 24:
24/9+1/9
24/9+1/9 = (24+1)/9:
(24+1)/9
24+1 = 25:
Answer: | 25/9
(3^2*2^3)*3^-3+(3/3^3)
[(9*8) * 1/27] + [3/27] =
[72/27] + [3/27] =
75/27 = divide both sides by 3
25/9 =2 7/9