Solve (-5m^2n/25mn^-1)^0

$$( - \frac { 5 m ^ { 2 } n } { 25 m n ^ { - 1 } } ) ^ { 0 }$$

Evaluate

$$1$$

Solution Steps

Cancel out 5m in both numerator and denominator.

$$\left(-\frac{mn}{5\times \frac{1}{n}}\right)^{0}$$

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

$$\left(-\frac{mn^{2}}{5}\right)^{0}$$

Expand \left(-\frac{mn^{2}}{5}\right)^{0}.

$$\left(-1\right)^{0}\times \left(\frac{mn^{2}}{5}\right)^{0}$$

Calculate -1 to the power of 0 and get 1.

$$1\times \left(\frac{mn^{2}}{5}\right)^{0}$$

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

$$1\times \frac{\left(mn^{2}\right)^{0}}{5^{0}}$$

Express 1\times \frac{\left(mn^{2}\right)^{0}}{5^{0}} as a single fraction.

$$\frac{\left(mn^{2}\right)^{0}}{5^{0}}$$

Calculate mn^{2} to the power of 0 and get 1.

$$\frac{1}{5^{0}}$$

Calculate 5 to the power of 0 and get 1.

$$\frac{1}{1}$$

Anything divided by one gives itself.

$$1$$

Factor

$$1$$