[tex]a) { ({5}^{2}) }^{4} \times {5}^{8} \div {5}^{15} [/tex]
[tex] = {5}^{2 \times 4} \times {5}^{8} \div {5}^{15} [/tex]
[tex] = {5}^{8} \times {5}^{8} \div {5}^{15} [/tex]
[tex] = {5}^{8 + 8 - 15} [/tex]
[tex] = {5}^{16 - 15} [/tex]
[tex] = {5}^{1} [/tex]
[tex] = 5[/tex]
[tex]b) {( {4}^{0} + {4}^{1} + {4}^{2} ) }^{5} \div {21}^{3} - {21}^{2} [/tex]
[tex] = {(1 + 4 + 16)}^{5} \div {21}^{3} - {21}^{2} [/tex]
[tex] = {21}^{5} \div {21}^{3} - {21}^{2} [/tex]
[tex] = {21}^{5 - 3} - {21}^{2} [/tex]
[tex] = {21}^{2} - {21}^{2} [/tex]
[tex] = 0[/tex]