a) \(A\cdot B\cdot C\)
\(=2a^2bc^3\cdot-3a^5b^2\cdot-\dfrac{1}{2}\cdot b^3c^4\)
\(=\left(2\cdot-3\cdot-\dfrac{1}{2}\right)\left(a^2\cdot a^5\right)\left(b\cdot b^2\cdot b^3\right)\left(c^3\cdot c^4\right)\)
\(=3a^7b^6c^7\)
b) \(A^2\cdot B\cdot C^3\)
\(=\left(2a^2bc^3\right)^2\cdot-3a^5b^2\cdot\left(-\dfrac{1}{2}b^3c^4\right)^3\)
\(=4a^4b^2c^6\cdot-3a^5b^2\cdot-\dfrac{1}{8}b^9c^{12}\)
\(=\left(4\cdot-3\cdot-\dfrac{1}{8}\right)\left(a^4\cdot a^5\right)\left(b^2\cdot b^2\cdot b^9\right)\left(c^6\cdot c^{12}\right)\)
\(=\dfrac{3}{2}a^9b^{13}c^{18}\)
c) \(A\cdot B^2\cdot C\)
\(=2a^2bc^3\cdot\left(-3a^5b^2\right)^2\cdot-\dfrac{1}{2}b^3c^4\)
\(=2a^2bc^3\cdot9a^{10}b^4\cdot-\dfrac{1}{2}b^3c^4\)
\(=\left(2\cdot-\dfrac{1}{2}\cdot9\right)\left(a^2\cdot a^{10}\right)\left(b\cdot b^4\cdot b^3\right)\left(c^3\cdot c^4\right)\)
\(=-9a^{12}b^8c^7\)
