Let's solve the expression step by step. The expression given is:
[
\frac{-3^3}{0.5} - \frac{2}{-3^2} \div 3 \times 0.5 - 6
]
First, we calculate each part:
Calculate ( -3^3 ):
[
-3^3 = -27
]
Calculate ( -3^2 ):
[
-3^2 = -9
]
Now, substitute these values into the expression:
[
\frac{-27}{0.5} - \frac{2}{-9} \div 3 \times 0.5 - 6
]
Next, calculate ( \frac{-27}{0.5} ):
[
\frac{-27}{0.5} = -27 \times 2 = -54
]
Now calculate ( \frac{2}{-9} ):
[
\frac{2}{-9} = -\frac{2}{9}
]
Next, we do the division ( -\frac{2}{9} \div 3 ):
[
-\frac{2}{9} \div 3 = -\frac{2}{9} \times \frac{1}{3} = -\frac{2}{27}
]
Now multiply that by ( 0.5 ):
[
-\frac{2}{27} \times 0.5 = -\frac{2}{27} \times \frac{1}{2} = -\frac{1}{27}
]
Now substitute back into the expression:
[
-54 - \left(-\frac{1}{27}\right) - 6
]
This can be simplified to:
[
-54 + \frac{1}{27} - 6
]
Combine the integer parts first:
[
-54 - 6 = -60
]
Now we need to add ( \frac{1}{27} ):
[
-60 + \frac{1}{27}
]
To add these, convert ( -60 ) into a fraction:
[
-60 = -\frac{1620}{27}
]
Now add:
[
-\frac{1620}{27} + \frac{1}{27} = -\frac{1620 - 1}{27} = -\frac{1619}{27}
]
So the final result of the expression is:
[
-\frac{1619}{27}
]
