Solve (10m^-2n/6mn^-4)^2

$$( \frac { 10 m ^ { - 2 } n } { 6 m n ^ { - 4 } } ) ^ { 2 }$$

Evaluate

$$\frac{25n^{10}}{9m^{6}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{5^{2}n^{10}}{\left(3m^{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25n^{10}}{\left(3m^{3}\right)^{2}}$$

Expand \left(3m^{3}\right)^{2}.

$$\frac{25n^{10}}{3^{2}\left(m^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{25n^{10}}{3^{2}m^{6}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{25n^{10}}{9m^{6}}$$

Expand

$$\frac{25n^{10}}{9m^{6}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{5^{2}n^{10}}{\left(3m^{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25n^{10}}{\left(3m^{3}\right)^{2}}$$

Expand \left(3m^{3}\right)^{2}.

$$\frac{25n^{10}}{3^{2}\left(m^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{25n^{10}}{3^{2}m^{6}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{25n^{10}}{9m^{6}}$$