12. \( 10 a^{\frac{7}{3}} b^{-1} \cdot 3 a^{\frac{5}{3}} b^{8} \)

Calculate or simplify the expression \( 10*a^(7/3)*b^(-1) * 3*a^(5/3)*b^(8) \). Simplify the expression by following steps: - step0: Solution: \(10a^{\frac{7}{3}}b^{-1}\times 3a^{\frac{5}{3}}b^{8}\) - step1: Multiply the terms: \(30a^{\frac{7}{3}}b^{-1}a^{\frac{5}{3}}b^{8}\) - step2: Multiply the terms: \(30a^{\frac{7}{3}+\frac{5}{3}}b^{-1}\times b^{8}\) - step3: Add the numbers: \(30a^{4}b^{-1}\times b^{8}\) - step4: Multiply the terms: \(30a^{4}b^{-1+8}\) - step5: Add the numbers: \(30a^{4}b^{7}\) The simplified form of the expression \(10a^{\frac{7}{3}}b^{-1} \cdot 3a^{\frac{5}{3}}b^{8}\) is \(30a^{4}b^{7}\).