Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve the given expression \(\left(15^{1/\pi}\right)^5\), we follow a step-by-step process.
First, interpret the notation correctly:
[tex]\[ \left(15^{1/\pi}\right)^5 \][/tex]
Next, remember the property of exponents which states: \((a^m)^n = a^{m \cdot n}\). We can use this property to simplify our expression. In our case, \(a = 15\), \(m = 1/\pi\), and \(n = 5\):
[tex]\[ \left(15^{1/\pi}\right)^5 = 15^{(1/\pi) \cdot 5} \][/tex]
Now we need the value of \((1/\pi) \cdot 5\):
[tex]\[ (1/\pi) \cdot 5 = \frac{5}{\pi} \][/tex]
Thus, our expression is simplified to:
[tex]\[ 15^{5/\pi} \][/tex]
Now let's evaluate \(15^{5/\pi}\). Given the true results, we know that:
[tex]\[ 15^{1/\pi} \approx 2.3678897349212167 \][/tex]
Raising this value to the power of 5 gives us:
[tex]\[ (2.3678897349212167)^5 \approx 74.44017305013445 \][/tex]
Hence, the value of the original expression \(\left(15^{1/\pi}\right)^5\) is approximately \(74.44\).
Since none of the provided options match this result exactly:
- A. 1
- B. 8
- C. 15
- D. 243
None of the given answer choices is correct.
First, interpret the notation correctly:
[tex]\[ \left(15^{1/\pi}\right)^5 \][/tex]
Next, remember the property of exponents which states: \((a^m)^n = a^{m \cdot n}\). We can use this property to simplify our expression. In our case, \(a = 15\), \(m = 1/\pi\), and \(n = 5\):
[tex]\[ \left(15^{1/\pi}\right)^5 = 15^{(1/\pi) \cdot 5} \][/tex]
Now we need the value of \((1/\pi) \cdot 5\):
[tex]\[ (1/\pi) \cdot 5 = \frac{5}{\pi} \][/tex]
Thus, our expression is simplified to:
[tex]\[ 15^{5/\pi} \][/tex]
Now let's evaluate \(15^{5/\pi}\). Given the true results, we know that:
[tex]\[ 15^{1/\pi} \approx 2.3678897349212167 \][/tex]
Raising this value to the power of 5 gives us:
[tex]\[ (2.3678897349212167)^5 \approx 74.44017305013445 \][/tex]
Hence, the value of the original expression \(\left(15^{1/\pi}\right)^5\) is approximately \(74.44\).
Since none of the provided options match this result exactly:
- A. 1
- B. 8
- C. 15
- D. 243
None of the given answer choices is correct.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.