(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: \[ \frac{16}{81} a^6 b^8 \]