Sure, let's solve the problem step-by-step.
First, we need to understand what [tex]\( 27^{\frac{4}{3}} \)[/tex] represents. This expression involves taking the base number 27 to the power of [tex]\( \frac{4}{3} \)[/tex].
1. Understanding the Exponent: The exponent [tex]\( \frac{4}{3} \)[/tex] can be broken down into two parts:
- The denominator (3) signifies that we take the cube root of 27.
- The numerator (4) indicates that we then raise that result to the power of 4.
2. Step by Step Calculation:
- Step 1: Compute the Cube Root:
[tex]\(\sqrt[3]{27} = 3\)[/tex]
(Since the cube root of 27 is 3)
- Step 2: Raise to the Power of 4:
[tex]\((3)^4 = 81\)[/tex]
So, [tex]\( 27^{\frac{4}{3}} = 81 \)[/tex].
Therefore, the correct answer is [tex]\( 81 \)[/tex].
