To evaluate the expression \((8 \times 10^2)(7.5 \times 10^4) / (5 \times 10^2)\), follow these steps:
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Multiply the numerators:
\[ (8 \times 10^2)(7.5 \times 10^4) = 8 \times 7.5 \times 10^{2+4} \]
Calculate \(8 \times 7.5\):
\[ 8 \times 7.5 = 60 \]
Thus,
\[ 8 \times 7.5 \times 10^{2+4} = 60 \times 10^6 \]
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Then divide by the denominator:
\[ \frac{60 \times 10^6}{5 \times 10^2} \]
This can be separated into two parts:
\[ \frac{60}{5} \times \frac{10^6}{10^2} \]
First, calculate \(\frac{60}{5}\):
\[ \frac{60}{5} = 12 \]
Then calculate \(\frac{10^6}{10^2}\):
\[ \frac{10^6}{10^2} = 10^{6-2} = 10^4 \]
Therefore, we have:
\[ 12 \times 10^4 \]
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Convert to scientific notation:
\(12\) can be expressed in scientific notation as \(1.2 \times 10^1\). Thus:
\[ 12 \times 10^4 = 1.2 \times 10^1 \times 10^4 = 1.2 \times 10^{1+4} = 1.2 \times 10^5 \]
So the final answer, in scientific notation, is:
\[ \boxed{1.2 \times 10^5} \]