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Popular Álgebra >

desarrollar (7-\sqrt[5]{x/(1977326743)})^{18}

Solución

desarrollar

(7 - 5 \frac{x}{1977326743})^{18}

Solución

7^{18} - 5 7^{74} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 5 x ^{11}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 5 x ^{16}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}}

Pasos de solución

(7 - 5 \frac{x}{1977326743})^{18}

Aplicar el teorema del binomio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 7, b = - 5 \frac{x}{1977326743}

= i = 0 \sum 18 (i 18) \cdot 7^{(18 - i)} (- 5 \frac{x}{1977326743})^{i}

Expandir sumatorio

= \frac{18 !}{0 ! ( 18 - 0 ) !} \cdot 7^{18} (- 5 \frac{x}{1977326743})^{0} + \frac{18 !}{1 ! ( 18 - 1 ) !} \cdot 7^{17} (- 5 \frac{x}{1977326743})^{1} + \frac{18 !}{2 ! ( 18 - 2 ) !} \cdot 7^{16} (- 5 \frac{x}{1977326743})^{2} + \frac{18 !}{3 ! ( 18 - 3 ) !} \cdot 7^{15} (- 5 \frac{x}{1977326743})^{3} + \frac{18 !}{4 ! ( 18 - 4 ) !} \cdot 7^{14} (- 5 \frac{x}{1977326743})^{4} + \frac{18 !}{5 ! ( 18 - 5 ) !} \cdot 7^{13} (- 5 \frac{x}{1977326743})^{5} + \frac{18 !}{6 ! ( 18 - 6 ) !} \cdot 7^{12} (- 5 \frac{x}{1977326743})^{6} + \frac{18 !}{7 ! ( 18 - 7 ) !} \cdot 7^{11} (- 5 \frac{x}{1977326743})^{7} + \frac{18 !}{8 ! ( 18 - 8 ) !} \cdot 7^{10} (- 5 \frac{x}{1977326743})^{8} + \frac{18 !}{9 ! ( 18 - 9 ) !} \cdot 7^{9} (- 5 \frac{x}{1977326743})^{9} + \frac{18 !}{10 ! ( 18 - 10 ) !} \cdot 7^{8} (- 5 \frac{x}{1977326743})^{10} + \frac{18 !}{11 ! ( 18 - 11 ) !} \cdot 7^{7} (- 5 \frac{x}{1977326743})^{11} + \frac{18 !}{12 ! ( 18 - 12 ) !} \cdot 7^{6} (- 5 \frac{x}{1977326743})^{12} + \frac{18 !}{13 ! ( 18 - 13 ) !} \cdot 7^{5} (- 5 \frac{x}{1977326743})^{13} + \frac{18 !}{14 ! ( 18 - 14 ) !} \cdot 7^{4} (- 5 \frac{x}{1977326743})^{14} + \frac{18 !}{15 ! ( 18 - 15 ) !} \cdot 7^{3} (- 5 \frac{x}{1977326743})^{15} + \frac{18 !}{16 ! ( 18 - 16 ) !} \cdot 7^{2} (- 5 \frac{x}{1977326743})^{16} + \frac{18 !}{17 ! ( 18 - 17 ) !} \cdot 7^{1} (- 5 \frac{x}{1977326743})^{17} + \frac{18 !}{18 ! ( 18 - 18 ) !} \cdot 7^{0} (- 5 \frac{x}{1977326743})^{18}

Simplificar

\frac{18 !}{0 ! ( 18 - 0 ) !} \cdot 7^{18} (- 5 \frac{x}{1977326743})^{0} : 7^{18}

Simplificar

\frac{18 !}{1 ! ( 18 - 1 ) !} \cdot 7^{17} (- 5 \frac{x}{1977326743})^{1} : - \frac{7 ^{17} \cdot 18 5 x}{5 1977326743}

Simplificar

\frac{18 !}{2 ! ( 18 - 2 ) !} \cdot 7^{16} (- 5 \frac{x}{1977326743})^{2} : 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2}

Simplificar

\frac{18 !}{3 ! ( 18 - 3 ) !} \cdot 7^{15} (- 5 \frac{x}{1977326743})^{3} : - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3}

Simplificar

\frac{18 !}{4 ! ( 18 - 4 ) !} \cdot 7^{14} (- 5 \frac{x}{1977326743})^{4} : 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4}

Simplificar

\frac{18 !}{5 ! ( 18 - 5 ) !} \cdot 7^{13} (- 5 \frac{x}{1977326743})^{5} : - \frac{7 ^{13} \cdot 1224 x}{282475249}

Simplificar

\frac{18 !}{6 ! ( 18 - 6 ) !} \cdot 7^{12} (- 5 \frac{x}{1977326743})^{6} : 7^{12} \cdot 18564 (5 \frac{x}{1977326743})^{6}

Simplificar

\frac{18 !}{7 ! ( 18 - 7 ) !} \cdot 7^{11} (- 5 \frac{x}{1977326743})^{7} : - 7^{11} \cdot 31824 (5 \frac{x}{1977326743})^{7}

Simplificar

\frac{18 !}{8 ! ( 18 - 8 ) !} \cdot 7^{10} (- 5 \frac{x}{1977326743})^{8} : 1.23606 E 13 (5 \frac{x}{1977326743})^{8}

Simplificar

\frac{18 !}{9 ! ( 18 - 9 ) !} \cdot 7^{9} (- 5 \frac{x}{1977326743})^{9} : - 1961992372340 (5 \frac{x}{1977326743})^{9}

Simplificar

\frac{18 !}{10 ! ( 18 - 10 ) !} \cdot 7^{8} (- 5 \frac{x}{1977326743})^{10} : \frac{252256162158 x ^{2}}{197732674 3 ^{2}}

Simplificar

\frac{18 !}{11 ! ( 18 - 11 ) !} \cdot 7^{7} (- 5 \frac{x}{1977326743})^{11} : - 26208432432 (5 \frac{x}{1977326743})^{11}

Simplificar

\frac{18 !}{12 ! ( 18 - 12 ) !} \cdot 7^{6} (- 5 \frac{x}{1977326743})^{12} : 2184036036 (5 \frac{x}{1977326743})^{12}

Simplificar

\frac{18 !}{13 ! ( 18 - 13 ) !} \cdot 7^{5} (- 5 \frac{x}{1977326743})^{13} : - 144002376 (5 \frac{x}{1977326743})^{13}

Simplificar

\frac{18 !}{14 ! ( 18 - 14 ) !} \cdot 7^{4} (- 5 \frac{x}{1977326743})^{14} : 7347060 (5 \frac{x}{1977326743})^{14}

Simplificar

\frac{18 !}{15 ! ( 18 - 15 ) !} \cdot 7^{3} (- 5 \frac{x}{1977326743})^{15} : - \frac{279888 x ^{3}}{197732674 3 ^{3}}

Simplificar

\frac{18 !}{16 ! ( 18 - 16 ) !} \cdot 7^{2} (- 5 \frac{x}{1977326743})^{16} : 7497 (5 \frac{x}{1977326743})^{16}

Simplificar

\frac{18 !}{17 ! ( 18 - 17 ) !} \cdot 7^{1} (- 5 \frac{x}{1977326743})^{17} : - 126 (5 \frac{x}{1977326743})^{17}

Simplificar

\frac{18 !}{18 ! ( 18 - 18 ) !} \cdot 7^{0} (- 5 \frac{x}{1977326743})^{18} : (5 \frac{x}{1977326743})^{18}

= 7^{18} - \frac{7 ^{17} \cdot 18 5 x}{5 1977326743} + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - \frac{7 ^{13} \cdot 1224 x}{282475249} + 7^{12} \cdot 18564 (5 \frac{x}{1977326743})^{6} - 7^{11} \cdot 31824 (5 \frac{x}{1977326743})^{7} + 1.23606 E 13 (5 \frac{x}{1977326743})^{8} - 1961992372340 (5 \frac{x}{1977326743})^{9} + \frac{252256162158 x ^{2}}{197732674 3 ^{2}} - 26208432432 (5 \frac{x}{1977326743})^{11} + 2184036036 (5 \frac{x}{1977326743})^{12} - 144002376 (5 \frac{x}{1977326743})^{13} + 7347060 (5 \frac{x}{1977326743})^{14} - \frac{279888 x ^{3}}{197732674 3 ^{3}} + 7497 (5 \frac{x}{1977326743})^{16} - 126 (5 \frac{x}{1977326743})^{17} + (5 \frac{x}{1977326743})^{18}

Simplificar

7^{18} - \frac{7 ^{17} \cdot 18 5 x}{5 1977326743} + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - \frac{7 ^{13} \cdot 1224 x}{282475249} + 7^{12} \cdot 18564 (5 \frac{x}{1977326743})^{6} - 7^{11} \cdot 31824 (5 \frac{x}{1977326743})^{7} + 1.23606 E 13 (5 \frac{x}{1977326743})^{8} - 1961992372340 (5 \frac{x}{1977326743})^{9} + \frac{252256162158 x ^{2}}{197732674 3 ^{2}} - 26208432432 (5 \frac{x}{1977326743})^{11} + 2184036036 (5 \frac{x}{1977326743})^{12} - 144002376 (5 \frac{x}{1977326743})^{13} + 7347060 (5 \frac{x}{1977326743})^{14} - \frac{279888 x ^{3}}{197732674 3 ^{3}} + 7497 (5 \frac{x}{1977326743})^{16} - 126 (5 \frac{x}{1977326743})^{17} + (5 \frac{x}{1977326743})^{18} : 7^{18} - 7^{\frac{74}{5}} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 x ^{\frac{11}{5}}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 x ^{\frac{16}{5}}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}}

= 7^{18} - 7^{\frac{74}{5}} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 x ^{\frac{11}{5}}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 x ^{\frac{16}{5}}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}}

Simplificar

7^{18} - 7^{\frac{74}{5}} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 x ^{\frac{11}{5}}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 x ^{\frac{16}{5}}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}} : 7^{18} - 5 7^{74} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 5 x ^{11}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 5 x ^{16}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}}

= 7^{18} - 5 7^{74} \cdot 18 5 x + 7^{16} \cdot 153 (5 \frac{x}{1977326743})^{2} - 7^{15} \cdot 816 (5 \frac{x}{1977326743})^{3} + 7^{14} \cdot 3060 (5 \frac{x}{1977326743})^{4} - 419832 x + 129948 x 5 \frac{x}{1977326743} - \frac{31824 x 5 x ^{2}}{5 197732674 3 ^{2}} + \frac{43758 x 5 x ^{3}}{7 5 197732674 3 ^{3}} - \frac{48620 x 5 x ^{4}}{49 5 197732674 3 ^{4}} + \frac{43758 x ^{2}}{678223072849} - \frac{31824 5 x ^{11}}{823543 \cdot 240 1 ^{2} 5 1977326743} + \frac{2652 x ^{2} 5 x ^{2}}{823543 \cdot 240 1 ^{2} 5 197732674 3 ^{2}} - \frac{1224 x ^{2} 5 x ^{3}}{117649 \cdot 1680 7 ^{2} 5 197732674 3 ^{3}} + \frac{3060 x ^{2} 5 x ^{4}}{240 1 ^{3} \cdot 34 3 ^{2} 5 197732674 3 ^{4}} - \frac{816 x ^{3}}{7 ^{30}} + \frac{153 5 x ^{16}}{4 9 ^{14} \cdot 343 5 1977326743} - \frac{18 x ^{3} 5 x ^{2}}{7 ^{32} 5 197732674 3 ^{2}} + \frac{x ^{3} ( 5 \frac{x}{1977326743} ) ^{3}}{197732674 3 ^{3}}

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