Solve (-3m^-3n^5/15mn^3)^-2

$$( \frac { - 3 m ^ { - 3 } n ^ { 5 } } { 15 m n ^ { 3 } } ) ^ { - 2 }$$

Evaluate

$$\frac{25m^{8}}{n^{4}}$$

Solution Steps

Cancel out 3n^{3} in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Cancel out -1 in both numerator and denominator.

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

To raise \frac{n^{2}}{-5m^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{n^{-4}}{\left(-5\right)^{-2}m^{-8}}$$

Calculate -5 to the power of -2 and get \frac{1}{25}.

$$\frac{n^{-4}}{\frac{1}{25}m^{-8}}$$

Expand

$$\frac{25m^{8}}{n^{4}}$$

Solution Steps

Cancel out 3n^{3} in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Cancel out -1 in both numerator and denominator.

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

To raise \frac{n^{2}}{-5m^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{n^{-4}}{\left(-5\right)^{-2}m^{-8}}$$

Calculate -5 to the power of -2 and get \frac{1}{25}.

$$\frac{n^{-4}}{\frac{1}{25}m^{-8}}$$