Question

c) [(-4)^72: 2^142 + (-3)^54 : 3^53 + (-5)^48 : 25^23] : (-2)^5 =​

Answer 1

Răspuns: - 1

$\displaystyle{[(-4)^{72}:2^{142}+(-3)^{54}:3^{53}+(-5)^{48}: 25^{23}]:(-2)^{5}}=\\\\\displaystyle{[(4)^{72}:2^{142}+(3)^{54}:3^{53}+(5)^{48}: (5^{2})^{23}]:(-2)^{5}}=\\\\\displaystyle{(2^{2\cdot72}:2^{142}+3^{54-53}+5^{48}: 5^{2\cdot23}):(-2)^{5}}=\\\\\displaystyle{(2^{144}:2^{142}+3^{1}+5^{48}: 5^{46}):(-2)^{5}}=\\\\\displaystyle{(2^{144-142}+3+5^{48-46}):(-2)^{5}}=\\\\\displaystyle{(2^{2}+3+5^{2}):(-2)^{5}}=\\\\\displaystyle{(4+3+25}):(-32)}=\\\\\displaystyle{32:(-32)}=\\\\\boxed{-1}$