Question

CALCULATI:
[(3 la puterea 7*3 la puterea 8-1):(27 la puterea 5-1)] la puterea 4

{[(8*9-24+7*6):5+9]:9-(42-4-6 la puterea 2)} la puterea 100

VA ROG AJUTATIMA

Answer 1

$\star){[( {3}^{7} \times {3}^{8} - 1) \div ( {27}^{5} - 1) ]}^{4}$

$= { \left \{( {3}^{7 + 8} - 1) \div [ { ({3}^{3} )}^{5} - 1] \right \} }^{4}$

$={ [( {3}^{15} - 1) \div ( {3}^{3 \times 5} - 1)]}^{4}$

$={ [( {3}^{15} - 1) \div ( {3}^{15} - 1)] }^{4}$

$= {1}^{4}$

$= 1$

$\star){\left \{[(8 \times 9 - 24 + 7 \times 6) \div 5 + 9] \div 9 - (42 - 4 - {6}^{2} ) \right \}}^{100}$

$= { \left \{[(72 - 24 + 42) \div 5 + 9] \div 9 - (38 - 36) \right \}}^{100}$

$= { \left \{[(48 + 42) \div 5 + 9] \div 9 - 2 \right \}}^{100}$

$= {[(90 \div 5 + 9)\div 9 - 2]}^{100}$

$= {[(18 + 9) \div 9 - 2]}^{100}$

$= {(27 \div 9 - 2)}^{100}$

$= {(3 - 2)}^{100}$

$= {1}^{100}$

$= 1$

Answer 2

=[(3^15-1):((3^3)^5-1)]^4=

=[(3^15-1):(3^15-1)]^4=

=1^4

=1