Solve 2/11*(1/3)^11*1/1-(frac{1{3})^2}

$$\frac { 2 } { 11 } \cdot ( \frac { 1 } { 3 } ) ^ { 11 } \cdot \frac { 1 } { 1 - ( \frac { 1 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{1}{866052}\approx 0.000001155$$

Solution Steps

Calculate \frac{1}{3} to the power of 11 and get \frac{1}{177147}.

$$\frac{2}{11}\times \frac{1}{177147}\times \frac{1}{1-\left(\frac{1}{3}\right)^{2}}$$

Multiply \frac{2}{11} times \frac{1}{177147} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{11\times 177147}\times \frac{1}{1-\left(\frac{1}{3}\right)^{2}}$$

Do the multiplications in the fraction \frac{2\times 1}{11\times 177147}.

$$\frac{2}{1948617}\times \frac{1}{1-\left(\frac{1}{3}\right)^{2}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{2}{1948617}\times \frac{1}{1-\frac{1}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{2}{1948617}\times \frac{1}{\frac{9}{9}-\frac{1}{9}}$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{1948617}\times \frac{1}{\frac{9-1}{9}}$$

Subtract 1 from 9 to get 8.

$$\frac{2}{1948617}\times \frac{1}{\frac{8}{9}}$$

Divide 1 by \frac{8}{9} by multiplying 1 by the reciprocal of \frac{8}{9}.

$$\frac{2}{1948617}\times 1\times \frac{9}{8}$$

Multiply 1 and \frac{9}{8} to get \frac{9}{8}.

$$\frac{2}{1948617}\times \frac{9}{8}$$

Multiply \frac{2}{1948617} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 9}{1948617\times 8}$$

Do the multiplications in the fraction \frac{2\times 9}{1948617\times 8}.

$$\frac{18}{15588936}$$

Reduce the fraction \frac{18}{15588936} to lowest terms by extracting and canceling out 18.

$$\frac{1}{866052}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 ^ {9} \cdot 11} = 1.1546650778475196 \times 10^{-6}$$