Question

repede!!Dau 50 de puncte!!​

Answer 1

Explicație pas cu pas:

36. a)

$- 5 \cdot \{2 + \left[ {( - 150)}^{3} \div {( - 75)}^{3} + {( - 5)}^{6} \times {4}^{6} \div {( - 20)}^{6} \right] \div ( - 3)\} =$

$= - 5 \cdot \{2 + \left[ {(2 \times 75)}^{3} \div {75}^{3} + {5}^{6} \times {4}^{6} \div {20}^{6} \right] \div ( - 3)\}$

$= - 5 \cdot \{2 + \left[ {2}^{3} \times {75}^{3} \div {75}^{3} + ({5} \times {4})^{6} \div {20}^{6} \right] \div ( - 3)\}$

$= - 5 \cdot \left[2 + ({2}^{3} + 20^{6} \div {20}^{6})\div ( - 3) \right]$

$= - 5 \cdot \left[2 + (8 + 1)\div ( - 3) \right]$

$= - 5 \cdot \left[2 + 9\div ( - 3) \right]$

$= - 5 \cdot (2 - 3)$

$= - 5 \cdot ( - 1) = 5$

b)

${( - 5)}^{30} \div \{ - 1 + 3 \cdot  \left[ {( - 5)}^{20} \div {25}^{10} + {( - 22 + 17)}^{15} \div ( - {125}^{5} ) \right] \} =$

$= {5}^{30} \div \{ - 1 + 3 \cdot  \left[ {5}^{20} \div {( {5}^{2} )}^{10} + {( - 5)}^{15} \div ( - {( {5}^{3} )}^{5} ) \right] \}$

$= {5}^{30} \div \{ - 1 + 3 \cdot  \left[ {5}^{20} \div {5}^{20} + {( - 5}^{15}) \div ( - {5}^{15} ) \right] \}$

$= {5}^{30} \div \left[- 1 + 3 \cdot (1 + 1) \right]$

$= {5}^{30} \div (- 1 + 3 \cdot 2)$

$= {5}^{30} \div (- 1 + 6)$

$= {5}^{30} \div 5 = {5}^{29}$

37.

$a = (2 - 2 \cdot 5) \cdot \left[ {( - 7)}^{42} \div {49}^{20} + 25 \div ( - {5}^{2} ) + 7 \cdot ( - {2}^{2} ) \right] \div 40 =$

$= (2 - 10) \cdot \left[ {7}^{42} \div {( {7}^{2} )}^{20} + 25 \div ( - 25) + 7 \cdot ( - 4) \right] \div 40$

$= ( - 8) \cdot ({7}^{42} \div {7}^{40} - 1 - 28) \div 40$

$= ( - 8) \cdot ({7}^{2} - 29) \div 40$

$= ( - 8) \cdot (49 - 29) \div 40$

$= ( - 8) \cdot 20 \div 40$

$= - 160 \div 40 = - 40$

$\implies a = - 40$

.$b = | - {3}^{2} | - { | - 3| }^{2} + \left[ - 12 - | - 5| + {6}^{4} \div {( - 3)}^{4} \right] + {32}^{12} \div {( - 4)}^{30} =$

$= {3}^{2} - {3}^{2} + \left[ - 12 - 5 + {(2 \times 3)}^{4} \div {3}^{4} \right] + {( {2}^{5} )}^{12} \div {( {2}^{2} )}^{30}$

$= 0 + (- 17 + {2}^{4} \times {3}^{4} \div {3}^{4}) + {2}^{60} \div {2}^{60}$

$= (- 17 + {2}^{4}) + 1$

$= - 17 + 16 + 1 = 0$

$\implies b = 0$

→

$a < b$