Solve m^-3+n^-3/mn^-2

$$\frac { m ^ { - 3 } + n ^ { - 3 } } { m n ^ { - 2 } }$$

Evaluate

$$\frac{n^{2}}{m^{4}}+\frac{1}{mn}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(n^{-3}m^{3}+1\right)m^{-3}}{n^{-2}m}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{n^{-3}m^{3}+1}{n^{-2}m^{4}}$$

Expand the expression.

$$\frac{1+\left(\frac{1}{n}m\right)^{3}}{n^{-2}m^{4}}$$

Express \frac{1}{n}m as a single fraction.

$$\frac{1+\left(\frac{m}{n}\right)^{3}}{n^{-2}m^{4}}$$

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

$$\frac{1+\frac{m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n^{3}}{n^{3}}.

$$\frac{\frac{n^{3}}{n^{3}}+\frac{m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

Since \frac{n^{3}}{n^{3}} and \frac{m^{3}}{n^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{n^{3}+m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

Express \frac{\frac{n^{3}+m^{3}}{n^{3}}}{n^{-2}m^{4}} as a single fraction.

$$\frac{n^{3}+m^{3}}{n^{3}n^{-2}m^{4}}$$

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

$$\frac{n^{3}+m^{3}}{n^{1}m^{4}}$$

Calculate n to the power of 1 and get n.

$$\frac{n^{3}+m^{3}}{nm^{4}}$$

Expand

$$\frac{n^{2}}{m^{4}}+\frac{1}{mn}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(n^{-3}m^{3}+1\right)m^{-3}}{n^{-2}m}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{n^{-3}m^{3}+1}{n^{-2}m^{4}}$$

Expand the expression.

$$\frac{1+\left(\frac{1}{n}m\right)^{3}}{n^{-2}m^{4}}$$

Express \frac{1}{n}m as a single fraction.

$$\frac{1+\left(\frac{m}{n}\right)^{3}}{n^{-2}m^{4}}$$

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

$$\frac{1+\frac{m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{n^{3}}{n^{3}}.

$$\frac{\frac{n^{3}}{n^{3}}+\frac{m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

Since \frac{n^{3}}{n^{3}} and \frac{m^{3}}{n^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{n^{3}+m^{3}}{n^{3}}}{n^{-2}m^{4}}$$

Express \frac{\frac{n^{3}+m^{3}}{n^{3}}}{n^{-2}m^{4}} as a single fraction.

$$\frac{n^{3}+m^{3}}{n^{3}n^{-2}m^{4}}$$

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

$$\frac{n^{3}+m^{3}}{n^{1}m^{4}}$$

Calculate n to the power of 1 and get n.

$$\frac{n^{3}+m^{3}}{nm^{4}}$$