Explicație pas cu pas:
1)
[tex]( {4}^{31} + 6 \times {32}^{12} - 5 \times {16}^{15} )\div ( {8}^{21} - 5 \times {8}^{20}) - 1 = \\ [/tex]
[tex]= \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 \\ [/tex]
[tex]= (4 \times {2}^{60} + 6 \times {2}^{60} - 5 \times {2}^{60} )\div \left[{( {2}^{3} )}^{20}(8 - 5) \right] - 1 \\ [/tex]
[tex]= \left[{2}^{60}(4 + 6 - 5) \right]\div ({2}^{60} \times 3) - 1 \\ [/tex]
[tex] = ( {2}^{60} \times 5) \div ( {2}^{60} \times 3) - 1 = \frac{5}{3} - 1 \\ [/tex]
[tex] = \frac{2}{3} \\ [/tex]
2)
