To solve [tex]\(27^{\frac{4}{3}}\)[/tex], we can follow these steps:
1. Understand the expression [tex]\(27^{\frac{4}{3}}\)[/tex]:
- The exponent [tex]\(\frac{4}{3}\)[/tex] can be broken down into two parts: [tex]\(\frac{4}{3} = 3\cdot \frac{1}{3}\)[/tex].
- This means we first take the cube root of 27 and then raise the result to the power of 4.
2. First, find the cube root of 27:
- The cube root of 27 is 3 (since [tex]\(3^3 = 27\)[/tex]).
3. Next, raise the result to the power of 4:
- We now have: [tex]\(3^4\)[/tex].
- Calculating [tex]\(3^4\)[/tex]: [tex]\(3^4 = 3 \times 3 \times 3 \times 3 = 81\)[/tex].
So, [tex]\(27^{\frac{4}{3}} = 81\)[/tex].
The correct answer is [tex]\( \boxed{81} \)[/tex].
