Solve (a^3/5m^2)^-4

$$( \frac { a ^ { 3 } } { 5 m ^ { 2 } } ) ^ { - 4 }$$

Evaluate

$$\frac{625m^{8}}{a^{12}}$$

Solution Steps

To raise \frac{a^{3}}{5m^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{3}\right)^{-4}}{\left(5m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{\left(5m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{5^{-4}\left(m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{5^{-4}m^{-8}}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{a^{-12}}{\frac{1}{625}m^{-8}}$$

Expand

$$\frac{625m^{8}}{a^{12}}$$

Solution Steps

To raise \frac{a^{3}}{5m^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{3}\right)^{-4}}{\left(5m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{\left(5m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{5^{-4}\left(m^{2}\right)^{-4}}$$

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

$$\frac{a^{-12}}{5^{-4}m^{-8}}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{a^{-12}}{\frac{1}{625}m^{-8}}$$