[tex]\frac{2^{7}\cdot (4^{5} \div 2^{3}) ^{2} }{8^{3} } =\frac{2^{7}\cdot (2^{10} \div 2^{3}) ^{2} }{8^{3} } =\frac{2^{7}\cdot (2^{10-3} ) ^{2} }{(2^{3} )^{3} }=\frac{2^{7}\cdot (2^{7} ) ^{2} }{(2 )^{3\cdot 3} }=\frac{2^{7}\cdot 2^{2\cdot 7} }{2^{9} }=\frac{2^{7}\cdot 2^{14} }{2^{9} }=\frac{2^{7+14} }{2^{9} } =\frac{2^{21} }{2^{9} } =2^{21-9} =2^{12} =2 \cdot 2\cdot 2\cdot 2\cdot 2 \cdot 2\cdot 2\cdot2 \cdot 2\cdot 2\cdot 2\cdot=4~096\\[/tex]
Korzystam ze wzorów:
[tex](x^{n} )^{m} =x^{n\cdot m} \\\\x^{n} \cdot x^{m} =x^{n+m}\\\\\frac{x^{n} }{x^{m} } =x^{n-m}[/tex]
[tex]gdy ~~n,m~~to~~dowolne~~liczby~~rzeczywiste~~oraz~~x>0~~to~~wtedy~~zachodza~~w/w~~rownosci.[/tex]
[tex]Mam ~~obliczyc ~~czwarta ~~czesc ~~tej~~liczby:\\2^{12} \div 4=2^{12} \div 2^{2} =\frac{2^{12} }{2^{2} } =2^{12-2} =2^{10} =1~024\\\\lub ~~~~4~096\div 4=1~024\\\\Odp.~~Szukana ~~liczba~~to:~~1~024.[/tex]
