[tex]a) {8}^{16} \div {(2 \times {2}^{2} \times {4}^{10} )}^{2} - {2}^{1} - {2}^{0} [/tex]
[tex] = { ({2}^{3}) }^{16} \div {[2 \times {2}^{2} \times {( {2}^{2}) }^{10} ]}^{2} - 2 - 1[/tex]
[tex] = {2}^{3 \times 16} \div {(2 \times {2}^{2} \times {2}^{2 \times 10} )}^{2} - 2 - 1[/tex]
[tex] = {2}^{48} \div{ (2 \times {2}^{2} \times {2}^{20} )}^{2} - 2 - 1[/tex]
[tex] = {2}^{48} \div { {(2}^{1 + 2 + 20}) }^{2} - 2 - 1[/tex]
[tex] = {2}^{48} \div { ({2}^{23} )}^{2} - 2 - 1[/tex]
[tex] = {2}^{48} \div {2}^{23 \times 2} - 2 - 1[/tex]
[tex] = {2}^{48} \div {2}^{46} - 2 - 1[/tex]
[tex] = {2}^{48 - 46} - 2 - 1[/tex]
[tex] = {2}^{2} - 2 - 1[/tex]
[tex] = 4 - 2 - 1[/tex]
[tex] = 2 - 1[/tex]
[tex] = 1[/tex]
[tex]b)( {10}^{10} - {10}^{9} ) \div ( {10}^{9} - {10}^{8} )[/tex]
[tex] = [ {10}^{9} (10 - 1)] \div [ {10}^{8} (10 - 1)][/tex]
[tex] = ( {10}^{9} \times 9) \div ( {10}^{8} \times 9)[/tex]
[tex] = ( {10}^{9} \div {10}^{8} )(9 \div 9)[/tex]
[tex] = {10}^{9 - 8} \times 1[/tex]
[tex] = {10}^{1} [/tex]
[tex] = 10[/tex]
[tex]c) {( {2}^{2} \times {2}^{4} )}^{2} \div {4}^{6} - {16}^{4} \div {8}^{5} \div {2}^{1} \div {2}^{0} [/tex]
[tex] = {( {2}^{2 + 4}) }^{2} \div {( {2}^{2}) }^{6} - { ({2}^{4} )}^{4} \div {( {2}^{3} )}^{5} \div 2 \div 1[/tex]
[tex] = { ({2}^{6}) }^{2} \div {2}^{2 \times 6} - {2}^{4 \times 4} \div {2}^{3 \times 5} \div 2[/tex]
[tex] = {2}^{6 \times 2} \div {2}^{12} - {2}^{16} \div {2}^{15} \div 2[/tex]
[tex] = {2}^{12} \div {2}^{12} - {2}^{16 - 15 - 1} [/tex]
[tex] = {2}^{12 - 12} - {2}^{1 - 1} [/tex]
[tex] = {2}^{0} - {2}^{0} [/tex]
[tex] = 1 - 1[/tex]
[tex] = 0[/tex]
