(2/3ab²)³2/3a³b²

To simplify the expression \((\frac{2}{3} ab^2)^3 \cdot \frac{2}{3} a^3 b^2\), we can follow these steps:

1. Simplify \((\frac{2}{3} ab^2)^3\): \[ \left(\frac{2}{3}\right)^3 (a)^3 (b^2)^3 = \frac{8}{27} a^3 b^6 \]

2. Combine with \(\frac{2}{3} a^3 b^2\): Now we multiply the result from step 1 by \(\frac{2}{3} a^3 b^2\): \[ \left(\frac{8}{27} a^3 b^6\right) \cdot \left(\frac{2}{3} a^3 b^2\right) \]

3. Multiply the coefficients: \[ \frac{8}{27} \cdot \frac{2}{3} = \frac{16}{81} \]

4. Multiply the powers of \(a\) and the powers of \(b\)**:

   • For \(a\): \[ a^3 \cdot a^3 = a^{3+3} = a^6 \]
   • For \(b\): \[ b^6 \cdot b^2 = b^{6+2} = b^8 \]

5. Combine everything: So, the final simplified expression is: \[ \frac{16}{81} a^6 b^8 \]

Thus, the simplified form of the expression \((\frac{2}{3} ab^2)^3 \cdot \frac{2}{3} a^3 b^2\) is: \[ \frac{16}{81} a^6 b^8 \]