To determine the value of the expression [tex]\( 27^{1 / 3} \)[/tex], we need to calculate the cube root of 27. Let's go through this step-by-step:
1. Understanding the Expression: The exponent [tex]\(\frac{1}{3}\)[/tex] means we are looking for the cube root of 27.
2. Defining Cube Root: The cube root of a number [tex]\( x \)[/tex], written as [tex]\( x^{1/3} \)[/tex], is a value that, when multiplied by itself three times (or cubed), gives the original number [tex]\( x \)[/tex].
3. Finding the Cube Root of 27:
- We need to find a number which, when raised to the power of 3, equals 27.
Let's denote this unknown number by [tex]\( y \)[/tex]. We have [tex]\( y^3 = 27 \)[/tex].
4. Checking Possible Values:
- If we try [tex]\( y = 3 \)[/tex]:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
- Since [tex]\( 3^3 = 27 \)[/tex], it confirms that [tex]\( y = 3 \)[/tex].
Therefore, [tex]\( 27^{1/3} = 3 \)[/tex].
Answer: A. 3
