Question

Calculati: a) (5 la puterea2-2 la puterea 5:2):3-1 la puterea 2019
b) (3la puterea 2x2^6-2 la puterea 5x6):12-2 la puterea 5;
c) (7 la puterea4-7 la puterea 3):(7 la puterea 2-7)-2 la puterea3x5

Answer 1

$a) \ (5^2-2^5:2):3-1^{2019}=\\ \\ =(25-32:2):3-1=\\ \\ =(25-16):3-1=\\ \\=9:3-1=\\ \\=3-1=\\ \\ =2$

$b) \ (3^2\cdot 2^6-2^5\cdot 6):12-2^5=\\ \\ =\frac{3^2\cdot 2^6-2^5\cdot 6}{12}-2^5=\\ \\ =\frac{3\cdot 2^2 \cdot 3\cdot 2^4 - 2\cdot 6 \cdot 2^4}{12}-2^5=\\ \\ =\frac{12\cdot 3\cdot 2^4 - 12\cdot 2^4}{12}-2^5=\\ \\ =\frac{12(3\cdot 2^4-2^4)}{12}-2^5=\\ \\ =\frac{2^4(3-1)}{1}-2^5=\\ \\ =2^4\cdot 2 -2^5=\\ \\ =2^5-2^5=\\ \\ =0$

$c) \ (7^4-7^3):(7^2-7)-2^3\cdot 5=\\ \\ =\frac{7^4-7^3}{7^2-7}-2^3\cdot 5=\\ \\ =\frac{7^3(7-1)}{7(7-1)}-2^3\cdot 5=\\ \\ =\frac{7^3}{7}-2^3\cdot 5=\\ \\ =7^2-8\cdot 5=\\ \\ =49-40=\\ \\ =9$