Solve frac{27(1-frac{1}3^5)}{1-1/3}=

$$\frac { 27 ( 1 - \frac { 1 } { 3 } ^ { 5 } ) } { 1 - \frac { 1 } { 3 } } =$$

Evaluate

$$\frac{121}{3}\approx 40.333333333$$

Solution Steps

Calculate \frac{1}{3} to the power of 5 and get \frac{1}{243}.

$$\frac{27\left(1-\frac{1}{243}\right)}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{243}{243}.

$$\frac{27\left(\frac{243}{243}-\frac{1}{243}\right)}{1-\frac{1}{3}}$$

Since \frac{243}{243} and \frac{1}{243} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27\times \frac{243-1}{243}}{1-\frac{1}{3}}$$

Subtract 1 from 243 to get 242.

$$\frac{27\times \frac{242}{243}}{1-\frac{1}{3}}$$

Express 27\times \frac{242}{243} as a single fraction.

$$\frac{\frac{27\times 242}{243}}{1-\frac{1}{3}}$$

Multiply 27 and 242 to get 6534.

$$\frac{\frac{6534}{243}}{1-\frac{1}{3}}$$

Reduce the fraction \frac{6534}{243} to lowest terms by extracting and canceling out 27.

$$\frac{\frac{242}{9}}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{242}{9}}{\frac{3}{3}-\frac{1}{3}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{242}{9}}{\frac{3-1}{3}}$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{242}{9}}{\frac{2}{3}}$$

Divide \frac{242}{9} by \frac{2}{3} by multiplying \frac{242}{9} by the reciprocal of \frac{2}{3}.

$$\frac{242}{9}\times \frac{3}{2}$$

Multiply \frac{242}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{242\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{242\times 3}{9\times 2}.

$$\frac{726}{18}$$

Reduce the fraction \frac{726}{18} to lowest terms by extracting and canceling out 6.

$$\frac{121}{3}$$

Factor

$$\frac{11 ^ {2}}{3} = 40\frac{1}{3} = 40.333333333333336$$