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Popular Álgebra >

desarrollar (6-\sqrt[4]{x/(2176782336)})^{18}

Solución

expand

Solución

6^{18} - 1410554953728 4 x + 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2} - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3} + 110160 x - 51408 x 4 \frac{x}{2176782336} + \frac{1547 x x}{3888} - \frac{5304 x 4 x ^{3}}{4 217678233 6 ^{3}} + \frac{2645878929408 x ^{2}}{217678233 6 ^{2}} - \frac{489977579520 x ^{2} 4 \frac{x}{2176782336}}{217678233 6 ^{2}} + \frac{1575288 x ^{2} x}{217678233 6 ^{2}} - \frac{8908683264 x ^{2} 4 x ^{3}}{217678233 6 ^{2} 4 217678233 6 ^{3}} + \frac{866121984 x ^{3}}{217678233 6 ^{3}} - \frac{66624768 x ^{3} 4 \frac{x}{2176782336}}{217678233 6 ^{3}} + \frac{85 x ^{3} x}{217678233 6 ^{3}} - \frac{176256 x ^{3} 4 x ^{3}}{217678233 6 ^{3} 4 217678233 6 ^{3}} + \frac{5508 x ^{4}}{217678233 6 ^{4}} - \frac{108 x ^{4} 4 \frac{x}{2176782336}}{217678233 6 ^{4}} + \frac{x ^{4} ( 4 \frac{x}{2176782336} ) ^{2}}{217678233 6 ^{4}}

Pasos de solución

(6 - 4 \frac{x}{2176782336})^{18}

Aplicar el teorema del binomio:

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

a = 6, b = - 4 \frac{x}{2176782336}

= i = 0 \sum 18 (i 18) \cdot 6^{(18 - i)} (- 4 \frac{x}{2176782336})^{i}

Expandir sumatorio

= \frac{18 !}{0 ! ( 18 - 0 ) !} \cdot 6^{18} (- 4 \frac{x}{2176782336})^{0} + \frac{18 !}{1 ! ( 18 - 1 ) !} \cdot 6^{17} (- 4 \frac{x}{2176782336})^{1} + \frac{18 !}{2 ! ( 18 - 2 ) !} \cdot 6^{16} (- 4 \frac{x}{2176782336})^{2} + \frac{18 !}{3 ! ( 18 - 3 ) !} \cdot 6^{15} (- 4 \frac{x}{2176782336})^{3} + \frac{18 !}{4 ! ( 18 - 4 ) !} \cdot 6^{14} (- 4 \frac{x}{2176782336})^{4} + \frac{18 !}{5 ! ( 18 - 5 ) !} \cdot 6^{13} (- 4 \frac{x}{2176782336})^{5} + \frac{18 !}{6 ! ( 18 - 6 ) !} \cdot 6^{12} (- 4 \frac{x}{2176782336})^{6} + \frac{18 !}{7 ! ( 18 - 7 ) !} \cdot 6^{11} (- 4 \frac{x}{2176782336})^{7} + \frac{18 !}{8 ! ( 18 - 8 ) !} \cdot 6^{10} (- 4 \frac{x}{2176782336})^{8} + \frac{18 !}{9 ! ( 18 - 9 ) !} \cdot 6^{9} (- 4 \frac{x}{2176782336})^{9} + \frac{18 !}{10 ! ( 18 - 10 ) !} \cdot 6^{8} (- 4 \frac{x}{2176782336})^{10} + \frac{18 !}{11 ! ( 18 - 11 ) !} \cdot 6^{7} (- 4 \frac{x}{2176782336})^{11} + \frac{18 !}{12 ! ( 18 - 12 ) !} \cdot 6^{6} (- 4 \frac{x}{2176782336})^{12} + \frac{18 !}{13 ! ( 18 - 13 ) !} \cdot 6^{5} (- 4 \frac{x}{2176782336})^{13} + \frac{18 !}{14 ! ( 18 - 14 ) !} \cdot 6^{4} (- 4 \frac{x}{2176782336})^{14} + \frac{18 !}{15 ! ( 18 - 15 ) !} \cdot 6^{3} (- 4 \frac{x}{2176782336})^{15} + \frac{18 !}{16 ! ( 18 - 16 ) !} \cdot 6^{2} (- 4 \frac{x}{2176782336})^{16} + \frac{18 !}{17 ! ( 18 - 17 ) !} \cdot 6^{1} (- 4 \frac{x}{2176782336})^{17} + \frac{18 !}{18 ! ( 18 - 18 ) !} \cdot 6^{0} (- 4 \frac{x}{2176782336})^{18}

Simplificar

\frac{18 !}{0 ! ( 18 - 0 ) !} \cdot 6^{18} (- 4 \frac{x}{2176782336})^{0} : 6^{18}

Simplificar

\frac{18 !}{1 ! ( 18 - 1 ) !} \cdot 6^{17} (- 4 \frac{x}{2176782336})^{1} : - \frac{6 ^{17} \cdot 18 4 x}{4 2176782336}

Simplificar

\frac{18 !}{2 ! ( 18 - 2 ) !} \cdot 6^{16} (- 4 \frac{x}{2176782336})^{2} : 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2}

Simplificar

\frac{18 !}{3 ! ( 18 - 3 ) !} \cdot 6^{15} (- 4 \frac{x}{2176782336})^{3} : - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3}

Simplificar

\frac{18 !}{4 ! ( 18 - 4 ) !} \cdot 6^{14} (- 4 \frac{x}{2176782336})^{4} : 110160 x

Simplificar

\frac{18 !}{5 ! ( 18 - 5 ) !} \cdot 6^{13} (- 4 \frac{x}{2176782336})^{5} : - 6^{13} \cdot 8568 (4 \frac{x}{2176782336})^{5}

Simplificar

\frac{18 !}{6 ! ( 18 - 6 ) !} \cdot 6^{12} (- 4 \frac{x}{2176782336})^{6} : 6^{12} \cdot 18564 (4 \frac{x}{2176782336})^{6}

Simplificar

\frac{18 !}{7 ! ( 18 - 7 ) !} \cdot 6^{11} (- 4 \frac{x}{2176782336})^{7} : - 1.15457 E 13 (4 \frac{x}{2176782336})^{7}

Simplificar

\frac{18 !}{8 ! ( 18 - 8 ) !} \cdot 6^{10} (- 4 \frac{x}{2176782336})^{8} : \frac{2645878929408 x ^{2}}{217678233 6 ^{2}}

Simplificar

\frac{18 !}{9 ! ( 18 - 9 ) !} \cdot 6^{9} (- 4 \frac{x}{2176782336})^{9} : - 489977579520 (4 \frac{x}{2176782336})^{9}

Simplificar

\frac{18 !}{10 ! ( 18 - 10 ) !} \cdot 6^{8} (- 4 \frac{x}{2176782336})^{10} : 73496636928 (4 \frac{x}{2176782336})^{10}

Simplificar

\frac{18 !}{11 ! ( 18 - 11 ) !} \cdot 6^{7} (- 4 \frac{x}{2176782336})^{11} : - 8908683264 (4 \frac{x}{2176782336})^{11}

Simplificar

\frac{18 !}{12 ! ( 18 - 12 ) !} \cdot 6^{6} (- 4 \frac{x}{2176782336})^{12} : \frac{866121984 x ^{3}}{217678233 6 ^{3}}

Simplificar

\frac{18 !}{13 ! ( 18 - 13 ) !} \cdot 6^{5} (- 4 \frac{x}{2176782336})^{13} : - 66624768 (4 \frac{x}{2176782336})^{13}

Simplificar

\frac{18 !}{14 ! ( 18 - 14 ) !} \cdot 6^{4} (- 4 \frac{x}{2176782336})^{14} : 3965760 (4 \frac{x}{2176782336})^{14}

Simplificar

\frac{18 !}{15 ! ( 18 - 15 ) !} \cdot 6^{3} (- 4 \frac{x}{2176782336})^{15} : - 176256 (4 \frac{x}{2176782336})^{15}

Simplificar

\frac{18 !}{16 ! ( 18 - 16 ) !} \cdot 6^{2} (- 4 \frac{x}{2176782336})^{16} : \frac{5508 x ^{4}}{217678233 6 ^{4}}

Simplificar

\frac{18 !}{17 ! ( 18 - 17 ) !} \cdot 6^{1} (- 4 \frac{x}{2176782336})^{17} : - 108 (4 \frac{x}{2176782336})^{17}

Simplificar

\frac{18 !}{18 ! ( 18 - 18 ) !} \cdot 6^{0} (- 4 \frac{x}{2176782336})^{18} : (4 \frac{x}{2176782336})^{18}

= 6^{18} - \frac{6 ^{17} \cdot 18 4 x}{4 2176782336} + 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2} - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3} + 110160 x - 6^{13} \cdot 8568 (4 \frac{x}{2176782336})^{5} + 6^{12} \cdot 18564 (4 \frac{x}{2176782336})^{6} - 1.15457 E 13 (4 \frac{x}{2176782336})^{7} + \frac{2645878929408 x ^{2}}{217678233 6 ^{2}} - 489977579520 (4 \frac{x}{2176782336})^{9} + 73496636928 (4 \frac{x}{2176782336})^{10} - 8908683264 (4 \frac{x}{2176782336})^{11} + \frac{866121984 x ^{3}}{217678233 6 ^{3}} - 66624768 (4 \frac{x}{2176782336})^{13} + 3965760 (4 \frac{x}{2176782336})^{14} - 176256 (4 \frac{x}{2176782336})^{15} + \frac{5508 x ^{4}}{217678233 6 ^{4}} - 108 (4 \frac{x}{2176782336})^{17} + (4 \frac{x}{2176782336})^{18}

Simplificar

6^{18} - \frac{6 ^{17} \cdot 18 4 x}{4 2176782336} + 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2} - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3} + 110160 x - 6^{13} \cdot 8568 (4 \frac{x}{2176782336})^{5} + 6^{12} \cdot 18564 (4 \frac{x}{2176782336})^{6} - 1.15457 E 13 (4 \frac{x}{2176782336})^{7} + \frac{2645878929408 x ^{2}}{217678233 6 ^{2}} - 489977579520 (4 \frac{x}{2176782336})^{9} + 73496636928 (4 \frac{x}{2176782336})^{10} - 8908683264 (4 \frac{x}{2176782336})^{11} + \frac{866121984 x ^{3}}{217678233 6 ^{3}} - 66624768 (4 \frac{x}{2176782336})^{13} + 3965760 (4 \frac{x}{2176782336})^{14} - 176256 (4 \frac{x}{2176782336})^{15} + \frac{5508 x ^{4}}{217678233 6 ^{4}} - 108 (4 \frac{x}{2176782336})^{17} + (4 \frac{x}{2176782336})^{18} : 6^{18} - 1410554953728 4 x + 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2} - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3} + 110160 x - 51408 x 4 \frac{x}{2176782336} + \frac{1547 x x}{3888} - \frac{5304 x 4 x ^{3}}{4 217678233 6 ^{3}} + \frac{2645878929408 x ^{2}}{217678233 6 ^{2}} - \frac{489977579520 x ^{2} 4 \frac{x}{2176782336}}{217678233 6 ^{2}} + \frac{1575288 x ^{2} x}{217678233 6 ^{2}} - \frac{8908683264 x ^{2} 4 x ^{3}}{217678233 6 ^{2} 4 217678233 6 ^{3}} + \frac{866121984 x ^{3}}{217678233 6 ^{3}} - \frac{66624768 x ^{3} 4 \frac{x}{2176782336}}{217678233 6 ^{3}} + \frac{85 x ^{3} x}{217678233 6 ^{3}} - \frac{176256 x ^{3} 4 x ^{3}}{217678233 6 ^{3} 4 217678233 6 ^{3}} + \frac{5508 x ^{4}}{217678233 6 ^{4}} - \frac{108 x ^{4} 4 \frac{x}{2176782336}}{217678233 6 ^{4}} + \frac{x ^{4} ( 4 \frac{x}{2176782336} ) ^{2}}{217678233 6 ^{4}}

= 6^{18} - 1410554953728 4 x + 6^{16} \cdot 153 (4 \frac{x}{2176782336})^{2} - 6^{15} \cdot 816 (4 \frac{x}{2176782336})^{3} + 110160 x - 51408 x 4 \frac{x}{2176782336} + \frac{1547 x x}{3888} - \frac{5304 x 4 x ^{3}}{4 217678233 6 ^{3}} + \frac{2645878929408 x ^{2}}{217678233 6 ^{2}} - \frac{489977579520 x ^{2} 4 \frac{x}{2176782336}}{217678233 6 ^{2}} + \frac{1575288 x ^{2} x}{217678233 6 ^{2}} - \frac{8908683264 x ^{2} 4 x ^{3}}{217678233 6 ^{2} 4 217678233 6 ^{3}} + \frac{866121984 x ^{3}}{217678233 6 ^{3}} - \frac{66624768 x ^{3} 4 \frac{x}{2176782336}}{217678233 6 ^{3}} + \frac{85 x ^{3} x}{217678233 6 ^{3}} - \frac{176256 x ^{3} 4 x ^{3}}{217678233 6 ^{3} 4 217678233 6 ^{3}} + \frac{5508 x ^{4}}{217678233 6 ^{4}} - \frac{108 x ^{4} 4 \frac{x}{2176782336}}{217678233 6 ^{4}} + \frac{x ^{4} ( 4 \frac{x}{2176782336} ) ^{2}}{217678233 6 ^{4}}

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