[tex]a) {( - 3)}^{101} + {3}^{101} = 0[/tex]
[tex]b) {( - 2)}^{3} + {( - 1001)}^{0} - {3}^{2} = - 8 + 0 - 9 = - 17[/tex]
[tex]c) {( - 343)}^{7} \times {7}^{23} \div {( - 49)}^{21} [/tex]
[tex] = { {( - 7}^{3} )}^{7} \times {7}^{23} \div { {( - 7}^{2} )}^{21} [/tex]
[tex] = {( - 7)}^{3 \times 7} \times {7}^{23} \div {( - 7)}^{2 \times 21} [/tex]
[tex] = {( - 7)}^{21} \times {7}^{23} \div {( - 7)}^{42} [/tex]
[tex] = - ( {7}^{21} \times {7}^{23} ) \div {( - 7)}^{42} [/tex]
[tex] = { - 7}^{21 + 23} \div {( - 7)}^{42} [/tex]
[tex] = { - 7}^{44} \div {( - 7)}^{42} [/tex]
[tex] = {( - 7)}^{44 - 42} [/tex]
[tex] = {( - 7)}^{2} [/tex]
[tex] = 49[/tex]
[tex]d) {( { - 5}^{2}) }^{5} \div {125}^{3} [/tex]
[tex] = {( - 5)}^{2 \times 5} \div { {(5}^{3} )}^{3} [/tex]
[tex] = {( - 5)}^{10} \div {5}^{3 \times 3} [/tex]
[tex] = {( - 5)}^{10} \div {5}^{9} [/tex]
[tex] = - ( {5}^{10} \div {5}^{9} )[/tex]
[tex] = - {5}^{10 - 9} [/tex]
[tex] = - {5}^{1} [/tex]
[tex] = - 5[/tex]
