Question

The value of $\frac{6^{12}\times {\left(35\right)}^{28}\times {\left(15\right)}^{16}}{{\left(14\right)}^{12}\times {\left(21\right)}^{11}\times 5^{28}}$ is __________.

Answer 1

$\frac{6^{12}\times {35}^{28}\times {15}^{16}}{{14}^{12}\times {21}^{11}\times 5^{28}}$

$=\frac{2^{12}\times 3^{12}\times 5^{28}\times 7^{28}\times 3^{16}\times 5^{16}}{2^{12}\times 7^{12}\times 3^{11}\times 7^{11}\times 5^{28}}$

$=\frac{2^{12}\times 3^{28}\times 5^{44}\times 7^{28}}{2^{12}\times 3^{11}\times 5^{28}\times 7^{23}}$

$=3^{28-11}\times 5^{44-28}\times 7^{28-23}$

$=3^{17}\times 5^{16}\times 7^5$(Ans)