Răspuns:
Explicație pas cu pas:
[tex]a) \: {3}^{100} \div {3}^{4} \div {3}^{6} \div {3}^{10} \div {3}^{7} = \\ = {3}^{100 - 4 - 6 - 10 - 7} \\ = {3}^{96 - 6 - 10 - 7} \\ = {3}^{90 - 10 - 7} \\ = {3}^{8 0 - 7} \\ = \boxed{ {3}^{73} }[/tex]
[tex]b) \: {13}^{4} \div 13 \div 13 \\ = {13}^{4} \div {13}^{1} \div {13}^{1} \\ = {13}^{4 - 1 - 1} \\ = {13}^{3 - 1} \\ = \boxed{ {13}^{2}} [/tex]
[tex]c) \: {8}^{9} \times {8}^{8} \div {8}^{10} \div {8}^{3} = \\ = {8}^{9 + 8 - 10 - 3} \\ = {8}^{17 - 10 - 3} \\ = {8}^{7 - 3} \\ = \boxed{ {8}^{4} }[/tex]
[tex]d) \: {12}^{5} \div {12}^{3} \times {12}^{6} \div {12}^{5} \div {12}^{2} = \\ = {12}^{5 - 3 + 6 - 5 - 2} \\ = {12}^{2 + 6 - 5 - 2} \\ = {12}^{8 - 5 - 2} \\ = {12}^{3 - 2} \\ = \boxed{ {12}^{1} }[/tex]
[tex]a) \: ( {3}^{4} )^{5} \times {3}^{5} = \\ = {3}^{4 \times 5} \times {3}^{5} \\ = {3}^{20} \times {3}^{5} \\ = {3}^{20 + 5} \\ = \boxed{ {3}^{25} }[/tex]
[tex]b) \: {16}^{4} \times {4}^{5} \div {2}^{5} = \\ = {( {2}^{4}) }^{4} \times {( {2}^{2} )}^{5} \div {2}^{5} \\ = {2}^{4 \times 4} \times {2}^{2 \times 5} \div {2}^{5} \\ = {2}^{16} \times {2}^{10} \div {2}^{5} \\ = {2}^{16 + 10 - 5} \\ = {2}^{26 - 5} \\ = \boxed{ {2}^{21} }[/tex]
Formule aplicate
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} \\ {a}^{m} \div {a}^{n} = {a}^{m - n} \\ {( {a}^{m} )}^{n} = {a}^{m \times n} [/tex]
