Let's evaluate each expression:
- \(|4| = 4\)
- \(\sqrt{9} = 3\)
- \(-3 = -3\)
- \(|-5| = 5\)
- \(-3^2 = -9\) (Note: This is interpreted as \(-(3^2) = -9\) because exponentiation has a higher precedence than negation.)
- \(2^3 = 8\)
Now we have the evaluated numbers:
- \(4\)
- \(3\)
- \(-3\)
- \(5\)
- \(-9\)
- \(8\)
Now, order these numbers from smallest to largest:
- \(-9\)
- \(-3\)
- \(3\)
- \(4\)
- \(5\)
- \(8\)
So the numbers ordered from smallest to largest are: \[ -9, -3, 3, 4, 5, 8 \]