Solve (6am^2/15a^3m)^4=

$$( \frac { 6 a m ^ { 2 } } { 15 a ^ { 3 } m } ) ^ { 4 } =$$

Evaluate

$$\frac{16m^{4}}{625a^{8}}$$

Solution Steps

Cancel out 3am in both numerator and denominator.

$$\left(\frac{2m}{5a^{2}}\right)^{4}$$

To raise \frac{2m}{5a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2m\right)^{4}}{\left(5a^{2}\right)^{4}}$$

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

$$\frac{2^{4}m^{4}}{\left(5a^{2}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16m^{4}}{\left(5a^{2}\right)^{4}}$$

Expand \left(5a^{2}\right)^{4}.

$$\frac{16m^{4}}{5^{4}\left(a^{2}\right)^{4}}$$

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

$$\frac{16m^{4}}{5^{4}a^{8}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{16m^{4}}{625a^{8}}$$

Expand

$$\frac{16m^{4}}{625a^{8}}$$

Solution Steps

Cancel out 3am in both numerator and denominator.

$$\left(\frac{2m}{5a^{2}}\right)^{4}$$

To raise \frac{2m}{5a^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2m\right)^{4}}{\left(5a^{2}\right)^{4}}$$

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

$$\frac{2^{4}m^{4}}{\left(5a^{2}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16m^{4}}{\left(5a^{2}\right)^{4}}$$

Expand \left(5a^{2}\right)^{4}.

$$\frac{16m^{4}}{5^{4}\left(a^{2}\right)^{4}}$$

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

$$\frac{16m^{4}}{5^{4}a^{8}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{16m^{4}}{625a^{8}}$$