Explicație pas cu pas:
[tex]({4}^{31} + 6 \cdot {32}^{12} - 5 \cdot {16}^{15}) \div ( {8}^{21} - 5 \cdot {8}^{20}) - 1 = \\ [/tex]
[tex]= ({( {2}^{2} )}^{31} + 6 \cdot {( {2}^{5} )}^{12} - 5 \cdot {( {2}^{4} )}^{15}) \div (8 \cdot {8}^{20} - 5 \cdot {8}^{20}) - 1 \\ [/tex]
[tex]= ({2}^{2\cdot 31} + 6 \cdot {2}^{5\cdot 12} - 5 \cdot {2}^{4\cdot 15}) \div \left[{8}^{20}\cdot (8 - 5) \right] - 1 \\ [/tex]
[tex]= ({2}^{62} + 6 \cdot {2}^{60} - 5 \cdot {2}^{60}) \div \left[3\cdot {( {2}^{3} )}^{20}\right] - 1 \\ [/tex]
[tex]= \left[{2}^{60} \cdot ( {2}^{2} + 6 - 5)\right] \div (3\cdot {2}^{3\cdot 20}) - 1 \\ [/tex]
[tex]= \left[{2}^{60} \cdot (4 + 6 - 5)\right] \div (3\cdot {2}^{60}) - 1 \\ [/tex]
[tex]= (5 \cdot {2}^{60}) \div (3\cdot {2}^{60}) - 1 \\ [/tex]
[tex] = \frac{5}{3} - 1 = \frac{5 - 3}{3} = \frac{2}{3} \\ [/tex]