Question

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Answer 1

17
$frac{6^n}{2^n*3^n} = frac{6^n}{6^n} =1$

18
 $frac{100^{n+2}}{10^{2n+3}} = frac{(10^2)^{n+2}}{10^{2n+3}} =frac{10^{2n+4}}{10^{2n+3}} =10$

19
$frac{63^{n+1}}{3^{2n+1}*7^{n-2}} = frac{7^{n+1}*3^{n+1}*3^{n+1}}{3^{2n+1}*7^{n-2}} =frac{7^{n+1}*3^{2n+2}}{3^{2n+1}*7^{n-2}} = \ 7^{n+1-(n-2)}*3^{2n+2-(2n+1)}=7^{n+1-n+2}*3^{2n+2-2n-1}=7^3*3= \ 343*3=1029$

20
$frac{80^{n+4}}{5^{n+3}*2^{4(n+3)+1}} = frac{5^{n+4}*16^{n+4}}{5^{n+3}*2^{4(n+3)+1}} = frac{5*(2^4)^{n+4}}{2^{4(n+3)+1}} = \ = frac{5*2^{4(n+4)}}{2^{4(n+3)+1}} = frac{5*2^{4n+16}}{2^{4n+13}} =5*2^{4n+16-4n-13}=5*2^3=5*8=40$

21
$frac{50^{n+1}}{2^{n-3}*5^{2n+1}} = frac{(5^2)^{n+1}*2^{n+1}}{2^{n-3}*5^{2n+1}} =frac{5^{2n+2}*2^{n+1}}{2^{n-3}*5^{2n+1}} =5^{2n+2-2n-1}*2^{n+1-n+3}= \ =5*2^4=5*4*4=20*4=80$