What is expand (1/2-(sqrt(3))/2)^{16} ?

The solution to expand (1/2-(sqrt(3))/2)^{16} is 18817/256-(679sqrt(3))/(16)

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expand (1/2-(sqrt(3))/2)^{16}

expand

(\frac{1}{2} - \frac{3}{2})^{16}

\frac{18817}{256} - \frac{679 3}{16}

Decimal Notation

1.03796 E - 7

Solution steps

(\frac{1}{2} - \frac{3}{2})^{16}

Apply binomial theorem:

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

a = \frac{1}{2}, b = - \frac{3}{2}

= i = 0 \sum 16 (i 16) (\frac{1}{2})^{(16 - i)} (- \frac{3}{2})^{i}

Expand summation

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

Simplify

\frac{16 !}{0 ! ( 16 - 0 ) !} (\frac{1}{2})^{16} (- \frac{3}{2})^{0} : \frac{1}{65536}

Simplify

\frac{16 !}{1 ! ( 16 - 1 ) !} (\frac{1}{2})^{15} (- \frac{3}{2})^{1} : - \frac{3}{4096}

Simplify

\frac{16 !}{2 ! ( 16 - 2 ) !} (\frac{1}{2})^{14} (- \frac{3}{2})^{2} : \frac{45}{8192}

Simplify

\frac{16 !}{3 ! ( 16 - 3 ) !} (\frac{1}{2})^{13} (- \frac{3}{2})^{3} : - \frac{105 3}{4096}

Simplify

\frac{16 !}{4 ! ( 16 - 4 ) !} (\frac{1}{2})^{12} (- \frac{3}{2})^{4} : \frac{4095}{16384}

Simplify

\frac{16 !}{5 ! ( 16 - 5 ) !} (\frac{1}{2})^{11} (- \frac{3}{2})^{5} : - \frac{2457 3}{4096}

Simplify

\frac{16 !}{6 ! ( 16 - 6 ) !} (\frac{1}{2})^{10} (- \frac{3}{2})^{6} : \frac{27027}{8192}

Simplify

\frac{16 !}{7 ! ( 16 - 7 ) !} (\frac{1}{2})^{9} (- \frac{3}{2})^{7} : - \frac{19305 3}{4096}

Simplify

\frac{16 !}{8 ! ( 16 - 8 ) !} (\frac{1}{2})^{8} (- \frac{3}{2})^{8} : \frac{521235}{32768}

Simplify

\frac{16 !}{9 ! ( 16 - 9 ) !} (\frac{1}{2})^{7} (- \frac{3}{2})^{9} : - \frac{57915 3}{4096}

Simplify

\frac{16 !}{10 ! ( 16 - 10 ) !} (\frac{1}{2})^{6} (- \frac{3}{2})^{10} : \frac{243243}{8192}

Simplify

\frac{16 !}{11 ! ( 16 - 11 ) !} (\frac{1}{2})^{5} (- \frac{3}{2})^{11} : - \frac{66339 3}{4096}

Simplify

\frac{16 !}{12 ! ( 16 - 12 ) !} (\frac{1}{2})^{4} (- \frac{3}{2})^{12} : \frac{331695}{16384}

Simplify

\frac{16 !}{13 ! ( 16 - 13 ) !} (\frac{1}{2})^{3} (- \frac{3}{2})^{13} : - \frac{25515 3}{4096}

Simplify

\frac{16 !}{14 ! ( 16 - 14 ) !} (\frac{1}{2})^{2} (- \frac{3}{2})^{14} : \frac{32805}{8192}

Simplify

\frac{16 !}{15 ! ( 16 - 15 ) !} (\frac{1}{2})^{1} (- \frac{3}{2})^{15} : - \frac{2187 3}{4096}

Simplify

\frac{16 !}{16 ! ( 16 - 16 ) !} (\frac{1}{2})^{0} (- \frac{3}{2})^{16} : \frac{6561}{65536}

= \frac{1}{65536} - \frac{3}{4096} + \frac{45}{8192} - \frac{105 3}{4096} + \frac{4095}{16384} - \frac{2457 3}{4096} + \frac{27027}{8192} - \frac{19305 3}{4096} + \frac{521235}{32768} - \frac{57915 3}{4096} + \frac{243243}{8192} - \frac{66339 3}{4096} + \frac{331695}{16384} - \frac{25515 3}{4096} + \frac{32805}{8192} - \frac{2187 3}{4096} + \frac{6561}{65536}

\frac{1}{65536} - \frac{3}{4096} + \frac{45}{8192} - \frac{105 3}{4096} + \frac{4095}{16384} - \frac{2457 3}{4096} + \frac{27027}{8192} - \frac{19305 3}{4096} + \frac{521235}{32768} - \frac{57915 3}{4096} + \frac{243243}{8192} - \frac{66339 3}{4096} + \frac{331695}{16384} - \frac{25515 3}{4096} + \frac{32805}{8192} - \frac{2187 3}{4096} + \frac{6561}{65536} = \frac{18817}{256} - \frac{679 3}{16}

= \frac{18817}{256} - \frac{679 3}{16}

cos (10 (t - 4))

(110 + 110 (1.732) i) \cdot \frac{9 - 27 i}{80 + 60 i = 9 - 27 i}

(x + \frac{1}{2})^{2} (x - 1 + 2)

e (k t + c)

(x - 2) d x

What is expand (1/2-(sqrt(3))/2)^{16} ?
The solution to expand (1/2-(sqrt(3))/2)^{16} is 18817/256-(679sqrt(3))/(16)