Question

1. a network engineer is calculating the total data output required for a new server. the client request rate is measured as 3k^{5}p^{2} operations per - minute. the server response rate is measured 10k^{4}p^{3} operations per - minute. the total workload is found by multiplying these two rates. what is the simplified expression for the total workload?

Explanation:

Step1: Multiply the two rates

The two rates are \(3k^{5}p^{2}\) and \(10k^{4}p^{3}\). When multiplying, use the rule \(a^{m}\times a^{n}=a^{m + n}\) for exponents.

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Step2: Calculate the coefficients and exponents

For the coefficients \(3\times10 = 30\). For the \(k\) - terms \(k^{5}\times k^{4}=k^{5 + 4}=k^{9}\). For the \(p\) - terms \(p^{2}\times p^{3}=p^{2+ 3}=p^{5}\).

Answer:

\(30k^{9}p^{5}\)