Solve {l}{(1/3)^6*40}{+20(1/3)^78}

$$\left. \begin{array} { l } { ( \frac { 1 } { 3 } ) ^ { 6 } \times 40 } \\ { + 20 ( \frac { 1 } { 3 } ) ^ { 7 } 8 } \end{array} \right.$$

Evaluate

$$\frac{280}{2187}\approx 0.128029264$$

Solution Steps

Calculate \frac{1}{3} to the power of 6 and get \frac{1}{729}.

$$\frac{1}{729}\times 40+20\times \left(\frac{1}{3}\right)^{7}\times 8$$

Multiply \frac{1}{729} and 40 to get \frac{40}{729}.

$$\frac{40}{729}+20\times \left(\frac{1}{3}\right)^{7}\times 8$$

Calculate \frac{1}{3} to the power of 7 and get \frac{1}{2187}.

$$\frac{40}{729}+20\times \frac{1}{2187}\times 8$$

Multiply 20 and \frac{1}{2187} to get \frac{20}{2187}.

$$\frac{40}{729}+\frac{20}{2187}\times 8$$

Express \frac{20}{2187}\times 8 as a single fraction.

$$\frac{40}{729}+\frac{20\times 8}{2187}$$

Multiply 20 and 8 to get 160.

$$\frac{40}{729}+\frac{160}{2187}$$

Least common multiple of 729 and 2187 is 2187. Convert \frac{40}{729} and \frac{160}{2187} to fractions with denominator 2187.

$$\frac{120}{2187}+\frac{160}{2187}$$

Since \frac{120}{2187} and \frac{160}{2187} have the same denominator, add them by adding their numerators.

$$\frac{120+160}{2187}$$

Add 120 and 160 to get 280.

$$\frac{280}{2187}$$

Factor

$$\frac{2 ^ {3} \cdot 5 \cdot 7}{3 ^ {7}} = 0.12802926383173296$$