Solve 27m^5n^4/(3mn^-2)^3=

$$\frac { 27 m ^ { 5 } n ^ { 4 } } { ( 3 m n ^ { - 2 } ) ^ { 3 } } =$$

Evaluate

$$m^{2}n^{10}$$

Solution Steps

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

$$\frac{27m^{5}n^{4}}{3^{3}m^{3}\left(n^{-2}\right)^{3}}$$

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

$$\frac{27m^{5}n^{4}}{3^{3}m^{3}n^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{5}n^{4}}{27m^{3}n^{-6}}$$

Cancel out 27m^{3} in both numerator and denominator.

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

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

$$m^{2}n^{10}$$

Expand

$$m^{2}n^{10}$$

Solution Steps

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

$$\frac{27m^{5}n^{4}}{3^{3}m^{3}\left(n^{-2}\right)^{3}}$$

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

$$\frac{27m^{5}n^{4}}{3^{3}m^{3}n^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{5}n^{4}}{27m^{3}n^{-6}}$$

Cancel out 27m^{3} in both numerator and denominator.

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

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

$$m^{2}n^{10}$$