Question

please help me with a b and c

Answer 1

$\frac{6^{21}\cdot10^7}{30^7} = \frac{(2\times3)^{21}\cdot(2\times5)^7}{(2\times3\times5)^7} = \frac{2^{21}\times3^{21}\times2^7\times5^7}{2^7\times3^7\times5^7} = 2^{21+7-7}\times3^{21-7}\times5^{7-7}\\=2^{21}\cdot3^{14}$

$\frac{6^{3m}\cdot10^m}{30^m} = \frac{(2\times3)^{3m}\cdot(2\times5)^m}{(2\times3\times5)^m} = \frac{2^{3m}\times3^{3m}\times2^m\times5^m}{2^m\times3^m\times5^m} \\= 2^{3m+m-m}\times3^{3m-m}\times5^{m-m}\\=2^{3m}\cdot3^{2m}$