Solve (m^4/5n^9)^3

$$( \frac { m ^ { 4 } } { 5 n ^ { 9 } } ) ^ { 3 }$$

Evaluate

$$\frac{m^{12}}{125n^{27}}$$

Solution Steps

To raise \frac{m^{4}}{5n^{9}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m^{4}\right)^{3}}{\left(5n^{9}\right)^{3}}$$

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

$$\frac{m^{12}}{\left(5n^{9}\right)^{3}}$$

Expand \left(5n^{9}\right)^{3}.

$$\frac{m^{12}}{5^{3}\left(n^{9}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{m^{12}}{5^{3}n^{27}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{m^{12}}{125n^{27}}$$

Expand

$$\frac{m^{12}}{125n^{27}}$$

Solution Steps

To raise \frac{m^{4}}{5n^{9}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m^{4}\right)^{3}}{\left(5n^{9}\right)^{3}}$$

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

$$\frac{m^{12}}{\left(5n^{9}\right)^{3}}$$

Expand \left(5n^{9}\right)^{3}.

$$\frac{m^{12}}{5^{3}\left(n^{9}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{m^{12}}{5^{3}n^{27}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{m^{12}}{125n^{27}}$$