Solve 1/9^2+1/9^3

$$\frac { 1 } { 9 ^ { 2 } } + \frac { 1 } { 9 ^ { 3 } }$$

Evaluate

$$\frac{10}{729}\approx 0.013717421$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\frac{1}{81}+\frac{1}{9^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{1}{81}+\frac{1}{729}$$

Least common multiple of 81 and 729 is 729. Convert \frac{1}{81} and \frac{1}{729} to fractions with denominator 729.

$$\frac{9}{729}+\frac{1}{729}$$

Since \frac{9}{729} and \frac{1}{729} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{729}$$

Add 9 and 1 to get 10.

$$\frac{10}{729}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {6}} = 0.013717421124828532$$