[tex]a) {( {2}^{2} \times 2 )}^{2} = {(2 ^{2 + 1}) }^{2} = {( {2}^{3} )}^{2} = {2}^{3 \times 2} = {2}^{6} [/tex]
[tex]b)( {4}^{3} \times 4 \times 4 ) \div ( {4}^{2} \times 4 ) = {4}^{3 + 1 + 1} \div {4}^{2 + 1} = {4}^{5} \div {4}^{3} = {4}^{5 - 3} = {4}^{2} = 16[/tex]
[tex]c) {( {5}^{4} )}^{2} \div {( {5}^{2} )}^{3} = {5}^{4 \times 2} \div {5}^{2 \times 3} = {5}^{8} \div {5}^{6} = {5}^{8 - 6} = {5}^{2} = 25[/tex]
[tex]d) {( {2}^{5} )}^{0} \times {( {2}^{2} )}^{2} = {2}^{5 \times 0} \times {2}^{2 \times 2} = {2}^{0} \times {2}^{4} = {2}^{0 + 4} = {2}^{4} = 16[/tex]
[tex]e) {( {2}^{7} \div {2}^{5} )}^{3} = {( {2}^{7 - 5} )}^{3} = {( {2}^{2} )}^{3} = {2}^{2 \times 3} = {2}^{6} [/tex]
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[tex]a) {( {2}^{2} \times 2 )}^{2} = {(2 ^{2 + 1}) }^{2} = {( {2}^{3} )}^{2} = {2}^{3 \times 2} = {2}^{6} [/tex]
[tex]b)( {4}^{3} \times 4 \times 4 ) \div ( {4}^{2} \times 4 ) = {4}^{3 + 1 + 1} \div {4}^{2 + 1} = {4}^{5} \div {4}^{3} = {4}^{5 - 3} = {4}^{2} = 16[/tex]
[tex]c) {( {5}^{4} )}^{2} \div {( {5}^{2} )}^{3} = {5}^{4 \times 2} \div {5}^{2 \times 3} = {5}^{8} \div {5}^{6} = {5}^{8 - 6} = {5}^{2} = 25[/tex]
[tex]d) {( {2}^{5} )}^{0} \times {( {2}^{2} )}^{2} = {2}^{5 \times 0} \times {2}^{2 \times 2} = {2}^{0} \times {2}^{4} = {2}^{0 + 4} = {2}^{4} = 16[/tex]
[tex]e) {( {2}^{7} \div {2}^{5} )}^{3} = {( {2}^{7 - 5} )}^{3} = {( {2}^{2} )}^{3} = {2}^{2 \times 3} = {2}^{6} [/tex]