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Popular >

expand (7/9+2/9)^9

Solution

expand

(\frac{7}{9} + \frac{2}{9})^{9}

Solution

1

Solution steps

(\frac{7}{9} + \frac{2}{9})^{9}

Apply binomial theorem:

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

a = \frac{7}{9}, b = \frac{2}{9}

= i = 0 \sum 9 (i 9) (\frac{7}{9})^{(9 - i)} (\frac{2}{9})^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} (\frac{7}{9})^{9} (\frac{2}{9})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (\frac{7}{9})^{8} (\frac{2}{9})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (\frac{7}{9})^{7} (\frac{2}{9})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (\frac{7}{9})^{6} (\frac{2}{9})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (\frac{7}{9})^{5} (\frac{2}{9})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (\frac{7}{9})^{4} (\frac{2}{9})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (\frac{7}{9})^{3} (\frac{2}{9})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (\frac{7}{9})^{2} (\frac{2}{9})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (\frac{7}{9})^{1} (\frac{2}{9})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (\frac{7}{9})^{0} (\frac{2}{9})^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (\frac{7}{9})^{9} (\frac{2}{9})^{0} : \frac{40353607}{387420489}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (\frac{7}{9})^{8} (\frac{2}{9})^{1} : \frac{11529602}{43046721}

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (\frac{7}{9})^{7} (\frac{2}{9})^{2} : \frac{13176688}{43046721}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (\frac{7}{9})^{6} (\frac{2}{9})^{3} : \frac{26353376}{129140163}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (\frac{7}{9})^{5} (\frac{2}{9})^{4} : \frac{3764768}{43046721}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (\frac{7}{9})^{4} (\frac{2}{9})^{5} : \frac{1075648}{43046721}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (\frac{7}{9})^{3} (\frac{2}{9})^{6} : \frac{614656}{129140163}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (\frac{7}{9})^{2} (\frac{2}{9})^{7} : \frac{25088}{43046721}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (\frac{7}{9})^{1} (\frac{2}{9})^{8} : \frac{1792}{43046721}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (\frac{7}{9})^{0} (\frac{2}{9})^{9} : \frac{512}{387420489}

= \frac{40353607}{387420489} + \frac{11529602}{43046721} + \frac{13176688}{43046721} + \frac{26353376}{129140163} + \frac{3764768}{43046721} + \frac{1075648}{43046721} + \frac{614656}{129140163} + \frac{25088}{43046721} + \frac{1792}{43046721} + \frac{512}{387420489}

\frac{40353607}{387420489} + \frac{11529602}{43046721} + \frac{13176688}{43046721} + \frac{26353376}{129140163} + \frac{3764768}{43046721} + \frac{1075648}{43046721} + \frac{614656}{129140163} + \frac{25088}{43046721} + \frac{1792}{43046721} + \frac{512}{387420489} = 1

= 1

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Frequently Asked Questions (FAQ)

What is expand (7/9+2/9)^9 ?
The solution to expand (7/9+2/9)^9 is 1