Question

Simplify $\frac{{12}^3\times {15}^2\times {20}^3}{6^4\times {10}^4\times 2^2}$.

Answer 1

$$\begin{gathered} \frac{{12}^3\times {15}^2\times {20}^3}{6^4\times {10}^4\times 2^2}=\frac{{\left(2^2\times 3\right)}^3\times {\left(5\times 3\right)}^2\times {\left(2^2\times 5\right)}^3}{{\left(3\times 2\right)}^4\times {\left(5\times 2\right)}^4\times 2^2} \\ =\frac{2^6\times 3^3\times 5^2\times 3^2\times 2^6\times 5^3}{3^4\times 2^4\times 5^4\times 2^4\times 2^2} \\ =\frac{2^{6+6}\times 3^{3+2}\times 5^{2+3}}{3^4\times 2^{4+4+2}\times 5^4} \\ =2^{12-10}\times 3^{5-4}\times 5^{5-4} \\ =2^2\times 3^1\times 5^1 \\ =60 \end{gathered}$$

Hence, the answer is $60$.