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]
