To simplify the expression \(\frac{2.16 \cdot 0.55 \cdot 4.5}{2.7 \cdot 0.15 \cdot 1.2}\), we'll start by calculating the numerator and the denominator separately.
Numerator:
\[ 2.16 \cdot 0.55 \cdot 4.5 \]
Calculate \(2.16 \cdot 0.55\): \[ 2.16 \cdot 0.55 = 1.188 \]
Now multiply the result by \(4.5\): \[ 1.188 \cdot 4.5 = 5.346 \]
Denominator:
\[ 2.7 \cdot 0.15 \cdot 1.2 \]
Calculate \(2.7 \cdot 0.15\): \[ 2.7 \cdot 0.15 = 0.405 \]
Now multiply the result by \(1.2\): \[ 0.405 \cdot 1.2 = 0.486 \]
Final Calculation:
Now, we can compute the fraction: \[ \frac{5.346}{0.486} \]
Calculating this gives: \[ 5.346 \div 0.486 \approx 11 \]
Therefore, the simplified value of the expression is approximately \(11\).