ABC26GN1966 · Surds and Indices

$\frac{6^{12} \times(35)^{28} \times(15)^{16}}{(14)^{12} \times(21)^{11}}=\frac{(2 \times 3)^{12} \times(5 \times 7)^{28} \times(3 \times 5)^{16}}{(2 \times 7)^{12} \times(3 \times 7)^{11}}$ $$\begin{aligned} & =\frac{2^{12} \times 3^{12} \times 5^{28} \times 7^{28} \times 3^{16} \times 5^{16}}{2^{12} \times 7^{12} \times 3^{11} \times 7^{11}} \\ & =2^{(12-12)} \times 3^{(12+16-11)} \times 5^{(28+16)} \times 7^{(28-12-11)} \\ & =2^{0} \times 3^{17} \times 5^{44} \times 7^{5}=3^{17} \times 5^{44} \times 7^{5} \end{aligned}$$ Number of prime factors $=17+44+5=66$.