Question

Efectuati:
$( {4}^{31} + 6 \times {32}^{12} - 5 \times {16}^{15} ) \div ( {8}^{21} - 5 \times {8}^{20}) - 1$
$( {25}^{4}) ^{3} \div {4}^{2} + {3}^{2} ) ^{11} - ( {0}^{2010} + {1}^{2012} + {2013}^{0}$
Va rog​

Answer 1

Explicație pas cu pas:

1)

$( {4}^{31} + 6 \times {32}^{12} - 5 \times {16}^{15} )\div ( {8}^{21} - 5 \times {8}^{20}) - 1 =$

$= \left[4 \times { ({2}^{2}) }^{30} + 6 \times {( {2}^{5} )}^{12} - 5 \times {( {2}^{5} )}^{15} \right]\div \left[8 \times {8}^{20} - 5 \times {8}^{20} ) \right] - 1$

$= (4 \times {2}^{60} + 6 \times {2}^{60} - 5 \times {2}^{60} )\div \left[{( {2}^{3} )}^{20}(8 - 5) \right] - 1$

$= \left[{2}^{60}(4 + 6 - 5) \right]\div ({2}^{60} \times 3) - 1$

$= ( {2}^{60} \times 5) \div ( {2}^{60} \times 3) - 1 = \frac{5}{3} - 1$

$= \frac{2}{3}$

2)