Solve (2m^2n^3/3p)^4

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

Evaluate

$$\frac{16m^{8}n^{12}}{81p^{4}}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{4}m^{8}\left(n^{3}\right)^{4}}{\left(3p\right)^{4}}$$

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

$$\frac{2^{4}m^{8}n^{12}}{\left(3p\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16m^{8}n^{12}}{\left(3p\right)^{4}}$$

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

$$\frac{16m^{8}n^{12}}{3^{4}p^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16m^{8}n^{12}}{81p^{4}}$$

Expand

$$\frac{16m^{8}n^{12}}{81p^{4}}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{4}m^{8}\left(n^{3}\right)^{4}}{\left(3p\right)^{4}}$$

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

$$\frac{2^{4}m^{8}n^{12}}{\left(3p\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16m^{8}n^{12}}{\left(3p\right)^{4}}$$

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

$$\frac{16m^{8}n^{12}}{3^{4}p^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16m^{8}n^{12}}{81p^{4}}$$