Pași de rezolvare:
[tex]2^{50}\cdot \frac{2}{\left(2^3\right)^7}[/tex]
[tex]\left(2^3\right)^7=2^{21}[/tex]
[tex]=\frac{2}{2^{21}}[/tex]
Renunță la factorul comun 2.
[tex]=\frac{1}{2^{20}}[/tex]
[tex]=2^{50}\cdot \frac{1}{2^{20}}[/tex]
Înmulțim regula fracțiilor:
[tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]=\frac{1\cdot \:2^{50}}{2^{20}}[/tex]
[tex]=\frac{2^{50}}{2^{20}}[/tex]
Aplicăm regula exponenților:
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]\frac{2^{50}}{2^{20}}=2^{50-20}[/tex]
[tex]=2^{50-20}[/tex]
Rezultat: [tex]=2^{30}[/tex] (1073741824)
b)
[tex]3^{17}\left(\frac{2\cdot \:5^2-2021}{43}\right)[/tex]
Renunțăm la paranteze:
[tex]=3^{17}\cdot \frac{2\cdot \:5^2-2021}{43}[/tex]
[tex]\frac{2\cdot \:5^2-2021}{43}[/tex]
[tex]2\cdot \:5^2-2021=-1971[/tex]
[tex]2\cdot \:5^2=50[/tex]
[tex]=50-2021=-1971[/tex]
[tex]=\frac{-1971}{43}[/tex]
Aplicăm regula fracțiilor:
[tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{1971}{43}[/tex]
[tex]=3^{17}\left(-\frac{1971}{43}\right)[/tex]
Renunțăm la paranteze:
[tex]=-3^{17}\cdot \frac{1971}{43}[/tex]
Înmulțim fracțiile:
[tex]=-\frac{1971\cdot \:3^{17}}{43}[/tex]
[tex]1971\cdot \:3^{17}=254535261273[/tex]
[tex]=-\frac{254535261273}{43}[/tex]
[tex]=-5919424680.76744[/tex]
a>b (a= 1073741824 , b= -5919424680.76744 )
b)
[tex]\frac{\begin{matrix}\space\space&\textbf{\space\space}&8&11&8&13&12&3&16&7&10&\space\space&\space\space&\space\space&\space\space&\space\space&\space\space\\ \space\space&\textbf{5}&\linethrough{9}&\linethrough{1}&\linethrough{9}&\linethrough{14}&\linethrough{2}&\linethrough{4}&\linethrough{6}&\linethrough{8}&\linethrough{0}&.&7&6&7&4&4\\ -&\textbf{1}&0&7&3&7&4&1&8&2&4&.&0&0&0&0&0\end{matrix}}{\begin{matrix}\space\space&\textbf{4}&8&4&5&6&8&2&8&5&6&.&7&6&7&4&4\end{matrix}}[/tex]
Nu se divide.
Sper că te-am ajutat!
Succes!
