Sure, let's simplify the expression step by step:
[tex]$
\frac{-5(3-\sqrt[3]{27} \cdot 2)}{3}
$[/tex]
1. Evaluate the cube root:
The cube root of 27 is 3 because \( \sqrt[3]{27} = 3 \).
2. Multiply the cube root result by 2:
\( \sqrt[3]{27} \cdot 2 = 3 \cdot 2 = 6 \).
3. Subtract the result from 3:
\( 3 - 6 = -3 \).
4. Multiply by -5:
\( -5 \cdot (-3) = 15 \).
5. Divide by 3:
\( \frac{15}{3} = 5 \).
So, the simplified expression is [tex]\( \boxed{5} \)[/tex].
