(-2 1/2а³b)*3 1/5a⁸b5

To simplify the expression \((-2 \frac{1}{2} a^3 b) \cdot (3 \frac{1}{5} a^8 b^5)\), we can break it down step by step. 1. **Convert the mixed numbers to improper fractions**: - \(-2 \frac{1}{2} = -\frac{5}{2}\) - \(3 \frac{1}{5} = \frac{16}{5}\) 2. **Rewrite the expression**: \[ \left(-\frac{5}{2} a^3 b\right) \cdot \left(\frac{16}{5} a^8 b^5\right) \] 3. **Multiply the coefficients**: \[ -\frac{5}{2} \cdot \frac{16}{5} = -\frac{5 \cdot 16}{2 \cdot 5} = -\frac{16}{2} = -8 \] 4. **Multiply the variables**: - For \(a^3 \cdot a^8\): Add the exponents \(3 + 8 = 11\), so \(a^{11}\). - For \(b \cdot b^5\): Add the exponents \(1 + 5 = 6\), so \(b^{6}\). 5. **Combine everything**: \[ -8 a^{11} b^6 \] Thus, the simplified expression is: \[ \boxed{-8 a^{11} b^6} \]