Question

Calculati : a.[(3 la puterea 4 -2³·10):1+5 la puterea 12 :25 la puterea 6 ·5]:2³ b.[(10²- 6²):4³+(7²-3²):10]:5 c.4 la puterea 25 : (2·2)+(5³+5³·95):96-11²

Answer 1

Răspuns:

a)

$\it [(3^{4} -2^{3} \cdot10):1+5^{12} :25^{6} \cdot5]:2^{3}\\\\\\\it [(81 -8 \cdot10):1+5^{12} :(5^{2})^{6} \cdot5]:8\\\\\\\it [(81 -80):1+5^{12} :5^{2\cdot6} \cdot5]:8\\\\\\\it (1:1+5^{12-12+1}):8\\\\\\\it (1+5^{1}):8\\\\\\\it 6:8 = \boxed{\it\dfrac{3}{4}}$      

b)

$\it [(10^{2} -6^{2} ):4^{3} +(7^{2} -3^{2}):10] :5\\\\\\\it [(100 -36 ):4^{3} +(49 -9):10] :5\\\\\\\it (64:64 +40:10) :5\\\\\\\it (1 +4) :5\\\\\\\it 5 :5\\\\\\\boxed{\it 1}$

c)

$\it 4^{25}: (2\cdot2)+(5^{3} +5^{3} \cdot95):96-11^{2} \\\\\\\it 4^{25}: 4+(5^{3} +95\cdot 5^{3}):96-121\\\\\\\it 4^{25-1}+96\cdot 5^{3}:96-121\\\\\\\it 4^{24}+ 5^{3}-121\\\\\\\it 4^{24}+ 125-121\\\\\\ \boxed{\it 4^{24}+ 4}$