To solve [tex]\(\left(\frac{2}{3}\right)^3\)[/tex], we need to find the cube of the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Understanding the Problem:
- We start with the fraction [tex]\(\frac{2}{3}\)[/tex].
- We need to raise this fraction to the power of 3, or cube it.
2. Cubing the Fraction:
- When we cube a fraction, we raise both the numerator and the denominator to the power of 3:
[tex]\[
\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3}
\][/tex]
3. Calculating the Powers:
- Calculate the cube of the numerator:
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
- Calculate the cube of the denominator:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
4. Forming the Resulting Fraction:
- Now, substitute these values back into the fraction:
[tex]\[
\left(\frac{2}{3}\right)^3 = \frac{8}{27}
\][/tex]
5. Decimal Representation:
- Convert the fraction [tex]\(\frac{8}{27}\)[/tex] to a decimal to get a numerical approximation. The approximate decimal form of [tex]\(\frac{8}{27}\)[/tex] is:
[tex]\[
0.2962962962962962
\][/tex]
So, [tex]\(\left(\frac{2}{3}\right)^3 = 0.2962962962962962\)[/tex].
