### Instruction: Find $\frac{2}{3} \left(\frac{2}{3}\right)^{2} \frac{2}{3}$.### Response: To simplify this expression, I need to apply the order of operations and the rules of exponents and fractions.
First, I'll simplify the parentheses by raising $\frac{2}{3}$ to the second power.
To do that, I multiply the numerator and the denominator by themselves: $\left(\frac{2}{3}\right)^{2} = \frac{2 \cdot 2}{3 \cdot 3} = \frac{4}{9}$.
Now I can rewrite the expression as $\frac{2}{3} \left(\frac{4}{9}\right) \frac{2}{3}$.
Next, I'll simplify the product of fractions by multiplying the numerators and the denominators: $\frac{2}{3} \left(\frac{4}{9}\right) \frac{2}{3} = \frac{2 \cdot 4 \cdot 2}{3 \cdot 9 \cdot 3} = \frac{16}{81}$.
This is the simplest form of the expression, so I'm done.