Solve -3m^3/n^4T(-m/n^2)^4

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

Evaluate

$$-\frac{3Tm^{7}}{n^{12}}$$

Solution Steps

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

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

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

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

Calculate -1 to the power of 4 and get 1.

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

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

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

Express 1\times \frac{m^{4}}{\left(n^{2}\right)^{4}} as a single fraction.

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

Multiply \frac{-3m^{3}T}{n^{4}} times \frac{m^{4}}{\left(n^{2}\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{-3m^{7}T}{n^{4}\left(n^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{-3m^{7}T}{n^{4}n^{8}}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{-3m^{7}T}{n^{12}}$$

Expand

$$-\frac{3Tm^{7}}{n^{12}}$$

Solution Steps

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

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

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

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

Calculate -1 to the power of 4 and get 1.

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

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

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

Express 1\times \frac{m^{4}}{\left(n^{2}\right)^{4}} as a single fraction.

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

Multiply \frac{-3m^{3}T}{n^{4}} times \frac{m^{4}}{\left(n^{2}\right)^{4}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{-3m^{7}T}{n^{4}\left(n^{2}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{-3m^{7}T}{n^{4}n^{8}}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{-3m^{7}T}{n^{12}}$$