To compute the expression
\[ \frac{(5.4 \times 10^4) \times (2.2 \times 10^7)}{4.5 \times 10^5}, \]
we can handle the multiplication and division of the numbers and the powers of ten separately.
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Multiply the coefficients: \[ 5.4 \times 2.2 = 11.88. \]
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Add the exponents of 10: \[ 10^4 \times 10^7 = 10^{(4+7)} = 10^{11}. \]
So the numerator becomes: \[ 11.88 \times 10^{11}. \]
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Now, we divide by the denominator \(4.5 \times 10^5\):
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The coefficients: \[ \frac{11.88}{4.5} \approx 2.64. \]
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Subtract the exponents of 10: \[ 10^{11} \div 10^5 = 10^{(11-5)} = 10^6. \]
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Putting it all together: \[ 2.64 \times 10^6. \]
So the final result is \[ \boxed{2.64 \times 10^6}. \]