[tex]\star){[( {3}^{7} \times {3}^{8} - 1) \div ( {27}^{5} - 1) ]}^{4} [/tex]
[tex] = { \left \{( {3}^{7 + 8} - 1) \div [ { ({3}^{3} )}^{5} - 1] \right \} }^{4} [/tex]
[tex] ={ [( {3}^{15} - 1) \div ( {3}^{3 \times 5} - 1)]}^{4} [/tex]
[tex] ={ [( {3}^{15} - 1) \div ( {3}^{15} - 1)] }^{4} [/tex]
[tex] = {1}^{4} [/tex]
[tex] = 1[/tex]
[tex] \star){\left \{[(8 \times 9 - 24 + 7 \times 6) \div 5 + 9] \div 9 - (42 - 4 - {6}^{2} ) \right \}}^{100} [/tex]
[tex] = { \left \{[(72 - 24 + 42) \div 5 + 9] \div 9 - (38 - 36) \right \}}^{100} [/tex]
[tex] = { \left \{[(48 + 42) \div 5 + 9] \div 9 - 2 \right \}}^{100} [/tex]
[tex] = {[(90 \div 5 + 9)\div 9 - 2]}^{100} [/tex]
[tex] = {[(18 + 9) \div 9 - 2]}^{100} [/tex]
[tex] = {(27 \div 9 - 2)}^{100} [/tex]
[tex] = {(3 - 2)}^{100} [/tex]
[tex] = {1}^{100} [/tex]
[tex] = 1[/tex]
