To multiply the numbers \( (7 \times 10^{-5}) \) and \( (5 \times 10^{8}) \), we can follow these steps:
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Multiply the coefficients: \[ 7 \times 5 = 35 \]
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Add the exponents of the powers of 10: \[ -5 + 8 = 3 \]
Putting these together, we get: \[ 35 \times 10^{3} \]
Now, we should express \( 35 \) in scientific notation. Since \( 35 = 3.5 \times 10^{1} \), we can rewrite \( 35 \times 10^{3} \) as: \[ 3.5 \times 10^{1} \times 10^{3} \]
Combining the powers of 10: \[ 3.5 \times 10^{(1 + 3)} = 3.5 \times 10^{4} \]
Thus, the final result in scientific notation is: \[ \boxed{3.5 \times 10^{4}} \]