Solve (3m^5/5n)^3

$$( \frac { 3 m ^ { 5 } } { 5 n } ) ^ { 3 }$$

Evaluate

$$\frac{27m^{15}}{125n^{3}}$$

Solution Steps

To raise \frac{3m^{5}}{5n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{5}\right)^{3}}{\left(5n\right)^{3}}$$

Expand \left(3m^{5}\right)^{3}.

$$\frac{3^{3}\left(m^{5}\right)^{3}}{\left(5n\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}m^{15}}{\left(5n\right)^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{15}}{\left(5n\right)^{3}}$$

Expand \left(5n\right)^{3}.

$$\frac{27m^{15}}{5^{3}n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{27m^{15}}{125n^{3}}$$

Expand

$$\frac{27m^{15}}{125n^{3}}$$

Solution Steps

To raise \frac{3m^{5}}{5n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3m^{5}\right)^{3}}{\left(5n\right)^{3}}$$

Expand \left(3m^{5}\right)^{3}.

$$\frac{3^{3}\left(m^{5}\right)^{3}}{\left(5n\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}m^{15}}{\left(5n\right)^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{15}}{\left(5n\right)^{3}}$$

Expand \left(5n\right)^{3}.

$$\frac{27m^{15}}{5^{3}n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{27m^{15}}{125n^{3}}$$