Solve (mn^3/p^2q)^4

$$( \frac { m n ^ { 3 } } { p ^ { 2 } q } ) ^ { 4 }$$

Evaluate

$$\frac{\left(\frac{m}{q}\right)^{4}n^{12}}{p^{8}}$$

Solution Steps

To raise \frac{mn^{3}}{p^{2}q} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(mn^{3}\right)^{4}}{\left(p^{2}q\right)^{4}}$$

Expand \left(mn^{3}\right)^{4}.

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

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

$$\frac{m^{4}n^{12}}{\left(p^{2}q\right)^{4}}$$

Expand \left(p^{2}q\right)^{4}.

$$\frac{m^{4}n^{12}}{\left(p^{2}\right)^{4}q^{4}}$$

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

$$\frac{m^{4}n^{12}}{p^{8}q^{4}}$$

Expand

$$\frac{\left(\frac{m}{q}\right)^{4}n^{12}}{p^{8}}$$

Solution Steps

To raise \frac{mn^{3}}{p^{2}q} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(mn^{3}\right)^{4}}{\left(p^{2}q\right)^{4}}$$

Expand \left(mn^{3}\right)^{4}.

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

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

$$\frac{m^{4}n^{12}}{\left(p^{2}q\right)^{4}}$$

Expand \left(p^{2}q\right)^{4}.

$$\frac{m^{4}n^{12}}{\left(p^{2}\right)^{4}q^{4}}$$

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

$$\frac{m^{4}n^{12}}{p^{8}q^{4}}$$