Question

Se dau numerele:
a =
${2}^{50} \times 2 \div ( {2}^{3} ) ^{7}$
b =
${3}^{17} \times (2 \times {5}^{2} - 2021 \div 43)$
a) Compara a si b

b) Stabileste daca a + b se divide sau nu cu 5​

Answer 1

Pași de rezolvare:

$2^{50}\cdot \frac{2}{\left(2^3\right)^7}$

$\left(2^3\right)^7=2^{21}$

$=\frac{2}{2^{21}}$

Renunță la factorul comun 2.

$=\frac{1}{2^{20}}$

$=2^{50}\cdot \frac{1}{2^{20}}$

Înmulțim regula fracțiilor:

$a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{1\cdot \:2^{50}}{2^{20}}$

$=\frac{2^{50}}{2^{20}}$

Aplicăm regula exponenților:

$\frac{x^a}{x^b}=x^{a-b}$

$\frac{2^{50}}{2^{20}}=2^{50-20}$

$=2^{50-20}$

Rezultat: $=2^{30}$ (1073741824)

b)

$3^{17}\left(\frac{2\cdot \:5^2-2021}{43}\right)$

Renunțăm la paranteze:

$=3^{17}\cdot \frac{2\cdot \:5^2-2021}{43}$

$\frac{2\cdot \:5^2-2021}{43}$

$2\cdot \:5^2-2021=-1971$

$2\cdot \:5^2=50$

$=50-2021=-1971$

$=\frac{-1971}{43}$

Aplicăm regula fracțiilor:

$\frac{-a}{b}=-\frac{a}{b}$

$=-\frac{1971}{43}$

$=3^{17}\left(-\frac{1971}{43}\right)$

Renunțăm la paranteze:

$=-3^{17}\cdot \frac{1971}{43}$

Înmulțim fracțiile:

$=-\frac{1971\cdot \:3^{17}}{43}$

$1971\cdot \:3^{17}=254535261273$

$=-\frac{254535261273}{43}$

$=-5919424680.76744$

a>b (a= 1073741824 , b= -5919424680.76744 )

b)

$\frac{\begin{matrix}\space\space&\textbf{\space\space}&8&11&8&13&12&3&16&7&10&\space\space&\space\space&\space\space&\space\space&\space\space&\space\space\\ \space\space&\textbf{5}&\linethrough{9}&\linethrough{1}&\linethrough{9}&\linethrough{14}&\linethrough{2}&\linethrough{4}&\linethrough{6}&\linethrough{8}&\linethrough{0}&.&7&6&7&4&4\\ -&\textbf{1}&0&7&3&7&4&1&8&2&4&.&0&0&0&0&0\end{matrix}}{\begin{matrix}\space\space&\textbf{4}&8&4&5&6&8&2&8&5&6&.&7&6&7&4&4\end{matrix}}$

Nu se divide.

Sper că te-am ajutat!

Succes!