Question

Упростите выражение:
1)5^2n+3*5^2n-1
_____________     =
      25^2n+1

2) 2^m*3^n-1-2^m-1*3^n
    __________________   =   
             2^m*3^n

Answer 1

$2) frac{2^{m}3^{n-1}-2^{m-1}3^{n}}{2^{m}3^{n}}= frac{2^{m} frac{3^{n}}{3} - frac{2^{m}}{2} 3^{n}}{2^{m}3^{n}}= frac{2*2^{m}3^{n}-3*2^{m}3{n}}{6*2^{m}3^{n}}=- frac{2^{m}3^{n}}{6*2^{m}3^{n}}=- frac{1}{6}$
$1) frac{5^{2n+3}5^{2n-1}}{25^{2n-1}}= frac{5^{2n+3+2n-1}}{(5^{2})^{2n-1}}= frac{5^{4n+2}}{5^{4n-2}}=5^{4n+2-4n+2}=5^{4}=625$