Sure, let's break down the solution step by step.
1. Calculate the exponent in [tex]\(2^{4 \times 2 - 1}\)[/tex]:
- First, perform the multiplication inside the exponent: [tex]\(4 \times 2 = 8\)[/tex].
- Then, subtract 1 from the result: [tex]\(8 - 1 = 7\)[/tex].
- So, [tex]\(2^{4 \times 2 - 1}\)[/tex] simplifies to [tex]\(2^7\)[/tex].
2. Calculate [tex]\(2^7\)[/tex]:
- [tex]\(2^7 = 128\)[/tex].
3. Calculate [tex]\(2^9\)[/tex]:
- [tex]\(2^9 = 512\)[/tex].
4. Multiply the results of [tex]\(2^7\)[/tex] and [tex]\(2^9\)[/tex]:
- [tex]\(2^7 \cdot 2^9 = 128 \cdot 512 = 65536\)[/tex].
5. Calculate [tex]\(3^4\)[/tex]:
- [tex]\(3^4 = 81\)[/tex].
6. Add the results of [tex]\(65536\)[/tex] and [tex]\(81\)[/tex]:
- [tex]\(65536 + 81 = 65617\)[/tex].
Putting all these steps together, we have:
[tex]\[
2^{4 \times 2 - 1} \cdot 2^9 + 3^4 = 65617
\][/tex]
