Sure! Let's break down the given expression step-by-step for clarity:
1. Calculate [tex]\(5^{\frac{5}{2}}\)[/tex]:
- First, note that [tex]\(\frac{5}{2}\)[/tex] is 2.5.
- So we need to calculate [tex]\(5^{2.5}\)[/tex].
- [tex]\(5^{2.5}\)[/tex] is equal to approximately 55.9017.
2. Calculate [tex]\(3^5\)[/tex]:
- [tex]\(3^5\)[/tex] means multiplying 3 by itself 5 times.
- [tex]\(3^5 = 3 \times 3 \times 3 \times 3 \times 3\)[/tex].
- This results in 243.
3. Multiply the results from the two calculations:
- Now we need to multiply the results of [tex]\(5^{2.5}\)[/tex] and [tex]\(3^5\)[/tex].
- So, we multiply 55.9017 by 243.
- [tex]\(55.9017 \times 243 \approx 13584.113\)[/tex].
Therefore, the value of [tex]\(5^{\frac{5}{2}} \times 3^5\)[/tex] is approximately 13584.113.
To summarize:
- [tex]\(5^{\frac{5}{2}} \approx 55.9017\)[/tex],
- [tex]\(3^5 = 243\)[/tex],
- and multiplying these results gives approximately 13584.113.
