To compute \((6.02 \times 10^{23}) \times (9.63 \times 10^{-2})\), you can use the laws of exponents to simplify the calculation.
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First, multiply the coefficients (the numbers in front): \[ 6.02 \times 9.63 = 57.9746 \]
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Next, multiply the powers of ten: \[ 10^{23} \times 10^{-2} = 10^{23 - 2} = 10^{21} \]
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Now, combine the results: \[ 57.9746 \times 10^{21} \]
You can express it in scientific notation: \[ 5.79746 \times 10^{22} \]
So, the final result is approximately: \[ 5.80 \times 10^{22} \] (when rounded to three significant figures).