To multiply the two numbers in scientific notation and then divide them, we'll follow these steps:
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Set up the expression: \[ \frac{9 \times 10^6}{12 \times 10^{10}} \]
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Separate the coefficients and the powers of ten:
- Coefficients: \(\frac{9}{12}\)
- Powers of ten: \(\frac{10^6}{10^{10}}\)
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Calculate the coefficients: \[ \frac{9}{12} = \frac{3}{4} = 0.75 \]
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Calculate the powers of ten: \[ \frac{10^6}{10^{10}} = 10^{6 - 10} = 10^{-4} \]
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Combine the results: \[ 0.75 \times 10^{-4} \]
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Convert \(0.75\) to scientific notation: \[ 0.75 = 7.5 \times 10^{-1} \]
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Combine with the power of ten: \[ 7.5 \times 10^{-1} \times 10^{-4} = 7.5 \times 10^{-5} \]
So, the final answer in scientific notation is: \[ \boxed{7.5 \times 10^{-5}} \]