To solve the expression [tex]\( 27^{\frac{2}{3}} \)[/tex], let’s go through the steps systematically:
1. Identify the Base and Exponent:
- The base is [tex]\( 27 \)[/tex].
- The exponent is [tex]\( \frac{2}{3} \)[/tex].
2. Rewrite the Exponent in a Usable Form:
- [tex]\( 27^{\frac{2}{3}} \)[/tex] can be interpreted as taking the cube root of 27 first, and then squaring the result. This is because [tex]\( \frac{2}{3} \)[/tex] can be expressed as [tex]\( 2 \times \frac{1}{3} \)[/tex].
3. Find the Cube Root of 27:
- The cube root of 27 is a number which, when multiplied by itself three times, gives 27.
- We know that [tex]\( 3 \times 3 \times 3 = 27 \)[/tex].
- Therefore, the cube root of 27 is 3.
4. Square the Result:
- Now we need to square the result of the cube root.
- [tex]\( 3^2 = 3 \times 3 = 9 \)[/tex].
Thus, [tex]\( 27^{\frac{2}{3}} = 9 \)[/tex].
Now, let’s look at the given options:
- 3
- 6
- 9
- 18
From our calculations, [tex]\( 27^{\frac{2}{3}} \)[/tex] equals 9. Therefore, the correct answer is:
[tex]\[
\boxed{9}
\][/tex]
