Solve [(1/n)^2+1]*1/n

$$[ ( \frac { 1 } { n } ) ^ { 2 } + 1 ] \cdot \frac { 1 } { n }$$

Evaluate

$$\frac{1}{n}+\frac{1}{n^{3}}$$

Short Solution Steps

To raise \frac{1}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\left(\frac{1^{2}}{n^{2}}+1\right)\times \frac{1}{n}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n^{2}}{n^{2}}.

$$\left(\frac{1^{2}}{n^{2}}+\frac{n^{2}}{n^{2}}\right)\times \frac{1}{n}$$

Since \frac{1^{2}}{n^{2}} and \frac{n^{2}}{n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{1^{2}+n^{2}}{n^{2}}\times \frac{1}{n}$$

Combine like terms in 1^{2}+n^{2}.

$$\frac{1+n^{2}}{n^{2}}\times \frac{1}{n}$$

Multiply \frac{1+n^{2}}{n^{2}} times \frac{1}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1+n^{2}}{n^{2}n}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Expand

$$\frac{1}{n}+\frac{1}{n^{3}}$$

Short Solution Steps

To raise \frac{1}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\left(\frac{1^{2}}{n^{2}}+1\right)\times \frac{1}{n}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n^{2}}{n^{2}}.

$$\left(\frac{1^{2}}{n^{2}}+\frac{n^{2}}{n^{2}}\right)\times \frac{1}{n}$$

Since \frac{1^{2}}{n^{2}} and \frac{n^{2}}{n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{1^{2}+n^{2}}{n^{2}}\times \frac{1}{n}$$

Combine like terms in 1^{2}+n^{2}.

$$\frac{1+n^{2}}{n^{2}}\times \frac{1}{n}$$

Multiply \frac{1+n^{2}}{n^{2}} times \frac{1}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1+n^{2}}{n^{2}n}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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