[tex]\displaystyle\bf\\c)\\2^1\times2^2\times2^3\times3^2\times5^6=\\\\=2^{1+2+3}\times5^6\times3^2=\\\\=2^6\times5^6\times3^2=\\\\=(2\times5)^6\times3^2=\\\\=(10)^6\times3^2=1000000\times9=\boxed{\bf9000000}\\\\\\d)\\2^1\times2^2\times2^3\times2^4\times5^1\times5^2\times5^3\times5^4:10^{10}=\\\\=2^{1+2+3+4}\times5^{1+2+3+4}:10^{10}=\\\\=2^{10}\times5^{10}:10^{10}=\\\\=(2\times5)^{10}:10^{10}=\\\\=(10)^{10}:10^{10}=\boxed{\bf1}[/tex]
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[tex]\displaystyle\bf\\e)\\64\times16\times32\times125\times125\times625\times625\times5:10^{13}=\\\\~~~~~64=2^6\\~~~~~16=2^4\\~~~~~32=2^5\\~~~~~125=5^3\\~~~~~625=5^4\\~~~~~5=5^1\\\\=2^6\times2^4\times2^5\times5^3\times5^3\times5^4\times5^4\times5^1:10^{13}=\\\\=2^{6+4+5}\times5^{3+3+4+4+1}:10^{13}=\\\\=2^{15}\times5^{15}:10^{13}=\\\\=(2\times5)^{15}:10^{13}=\\\\=(10)^{15}:10^{13}=10^{15-13}=10^2=\boxed{\bf100}[/tex]
