To simplify the exponential expression [tex]\( 27^{\frac{1}{3}} \)[/tex], let's break down the problem step-by-step:
1. Understand the Exponential Expression:
The expression [tex]\( 27^{\frac{1}{3}} \)[/tex] involves raising 27 to the power of [tex]\( \frac{1}{3} \)[/tex].
2. Interpret the Power [tex]\( \frac{1}{3} \)[/tex]:
Raising a number to the power of [tex]\( \frac{1}{3} \)[/tex] means taking the cube root of the number. Therefore, [tex]\( 27^{\frac{1}{3}} \)[/tex] can be interpreted as the cube root of 27.
3. Find the Cube Root:
To find the cube root of 27, we need to determine what number, when multiplied by itself three times, equals 27. In other words, we are looking for a number [tex]\( x \)[/tex] such that [tex]\( x^3 = 27 \)[/tex].
4. Determine the Value:
By inspection or knowledge of basic cube roots, we know that [tex]\( 3^3 = 27 \)[/tex]. Therefore, the cube root of 27 is 3.
Thus, the simplified value of the exponential expression [tex]\( 27^{\frac{1}{3}} \)[/tex] is [tex]\( 3 \)[/tex].
The correct answer is:
[tex]\[ \boxed{3} \][/tex]
