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Popular >

expand (5/6+1/6)^4

Solution

expand

(\frac{5}{6} + \frac{1}{6})^{4}

Solution

1

Solution steps

(\frac{5}{6} + \frac{1}{6})^{4}

Apply binomial theorem:

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

a = \frac{5}{6}, b = \frac{1}{6}

= i = 0 \sum 4 (i 4) (\frac{5}{6})^{(4 - i)} (\frac{1}{6})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (\frac{5}{6})^{4} (\frac{1}{6})^{0} : \frac{625}{1296}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (\frac{5}{6})^{3} (\frac{1}{6})^{1} : \frac{125}{324}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (\frac{5}{6})^{2} (\frac{1}{6})^{2} : \frac{25}{216}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (\frac{5}{6})^{1} (\frac{1}{6})^{3} : \frac{5}{324}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (\frac{5}{6})^{0} (\frac{1}{6})^{4} : \frac{1}{1296}

= \frac{625}{1296} + \frac{125}{324} + \frac{25}{216} + \frac{5}{324} + \frac{1}{1296}

\frac{625}{1296} + \frac{125}{324} + \frac{25}{216} + \frac{5}{324} + \frac{1}{1296} = 1

= 1

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Frequently Asked Questions (FAQ)

What is expand (5/6+1/6)^4 ?
The solution to expand (5/6+1/6)^4 is 1