Răspuns:
a) 5; b) 25; c) 0; d) 3; e) 0; f) -27; g) 0; h) 0
Explicație pas cu pas:
a)
[tex] {6}^{2} \div ( - 9) + {3}^{2} = 36 \div ( - 9) + 9 = - 4 + 9 = 5[/tex]
b)
[tex] {5}^{8} \div ( {5}^{4} \times {5}^{2}) = {5}^{8} \div {5}^{4 + 2} = {5}^{8} \div {5}^{6} = {5}^{8 - 6} = {5}^{2} = 25[/tex]
c)
[tex]( - {4}^{2} ) \times {4}^{3} - {4}^{5} = {4}^{2} \times {4}^{3} - {4}^{5} = {4}^{2 + 3} - {4}^{5} = {4}^{5} - {4}^{5} = 0[/tex]
d)
[tex]( {3}^{4} \times {3}^{8} ) \div (( - {3}^{7} ) \div ( - {3}^{5} ) \times ( {3}^{9} )) = {3}^{4 + 8} \div ( {3}^{7 - 5} \times {3}^{9} ) = {3}^{12} \div ( {3}^{2} \times {3}^{9} ) = {3}^{12} \div {3}^{2 + 9} = {3}^{12} \div {3}^{11} = {3}^{12 - 11} = {3}^{1} = 3[/tex]
e)
[tex] {( - 8 + 1)}^{4} \times {7}^{3} \div {7}^{5} - {7}^{2} = {( - 7)}^{4} \times {7}^{3} \div {7}^{5} - {7}^{2} ={7}^{4} \times {7}^{3} \div {7}^{5} - {7}^{2} ={7}^{4 + 3} \div {7}^{5} - {7}^{2} ={7}^{7} \div {7}^{5} - {7}^{2} ={7}^{7 - 5} - {7}^{2} ={7}^{2} - {7}^{2} =0[/tex]
f)
[tex] {(2 - 5)}^{7} \times {( - 3}^{9}) \times {3}^{10} \div ( - {3}^{23} ) = {( - 3)}^{7} \times {( - 3}^{9}) \times {3}^{10} \div ( - {3}^{23} ) = {3}^{7} \times {3}^{9} \times {3}^{10} \div ( - {3}^{23} ) = - {3}^{7 + 9 + 10} \div {3}^{23} = - {3}^{26} \div {3}^{23} = - {3}^{26 - 23} = - {3}^{3} = - 27[/tex]
g)
[tex] {5}^{3} \times {5}^{6} - {5}^{7} \times {( - 5)}^{2} = {5}^{3 + 6} - {5}^{7} \times {5}^{2} = {5}^{9} - {5}^{7 + 2} = {5}^{9} - {5}^{9} = 0[/tex]
h)
[tex] {(1 - 3)}^{2} \times {2}^{5} \times {( - 2)}^{6} - {2}^{10} \times {2}^{3} = {( - 2)}^{2} \times {2}^{5} \times {2}^{6} - {2}^{10 + 3} = {2}^{2} \times {2}^{5} \times {2}^{6} - {2}^{13} = {2}^{2 + 5 + 6} \times {2}^{13} = {2}^{13} - {2}^{13} = 0[/tex]
