Solve (6/3*m/m^-1*n^-2/n^2)^-3

$$( \frac { 6 } { 3 } \cdot \frac { m } { m ^ { - 1 } } \cdot \frac { n ^ { - 2 } } { n ^ { 2 } } ) ^ { - 3 }$$

Evaluate

$$\frac{n^{12}}{8m^{6}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 1 to get 2.

$$\left(\frac{6}{3}m^{2}\times \frac{n^{-2}}{n^{2}}\right)^{-3}$$

Rewrite n^{2} as n^{-2}n^{4}. Cancel out n^{-2} in both numerator and denominator.

$$\left(\frac{6}{3}m^{2}\times \frac{1}{n^{4}}\right)^{-3}$$

Divide 6 by 3 to get 2.

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

Express 2\times \frac{1}{n^{4}} as a single fraction.

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

Expand \left(\frac{2}{n^{4}}m^{2}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\left(\frac{2}{n^{4}}\right)^{-3}m^{-6}$$

To raise \frac{2}{n^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{-3}}{\left(n^{4}\right)^{-3}}m^{-6}$$

Express \frac{2^{-3}}{\left(n^{4}\right)^{-3}}m^{-6} as a single fraction.

$$\frac{2^{-3}m^{-6}}{\left(n^{4}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{2^{-3}m^{-6}}{n^{-12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}m^{-6}}{n^{-12}}$$

Expand

$$\frac{n^{12}}{8m^{6}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 1 to get 2.

$$\left(\frac{6}{3}m^{2}\times \frac{n^{-2}}{n^{2}}\right)^{-3}$$

Rewrite n^{2} as n^{-2}n^{4}. Cancel out n^{-2} in both numerator and denominator.

$$\left(\frac{6}{3}m^{2}\times \frac{1}{n^{4}}\right)^{-3}$$

Divide 6 by 3 to get 2.

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

Express 2\times \frac{1}{n^{4}} as a single fraction.

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

Expand \left(\frac{2}{n^{4}}m^{2}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\left(\frac{2}{n^{4}}\right)^{-3}m^{-6}$$

To raise \frac{2}{n^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2^{-3}}{\left(n^{4}\right)^{-3}}m^{-6}$$

Express \frac{2^{-3}}{\left(n^{4}\right)^{-3}}m^{-6} as a single fraction.

$$\frac{2^{-3}m^{-6}}{\left(n^{4}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{2^{-3}m^{-6}}{n^{-12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}m^{-6}}{n^{-12}}$$