38.162/124.83
= 38.(24)2/(22.3)4.(23)3
= 38.28/28.34.29
=34/29
=81/512
\(\frac{3^8\cdot16^2}{12^4\cdot8^3}\)
\(=\frac{3^8\cdot2^8}{3^4\cdot2^8\cdot2^9}\)
\(=\frac{81}{512}\)
\(=\frac{3^8.\left(2^4\right)^2}{\left(3.4\right)^4.\left(2^3\right)^3}=\frac{3^8.2^8}{3^4.\left(2^2\right)^4.2^9}=\frac{3^4}{2^9}=\frac{81}{512}\)