Solve (-mn^3)^2*(-3m^2)^3

$$( - m n ^ { 3 } ) ^ { 2 } \cdot ( - 3 m ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-27n^{6}m^{8}$$

Solution Steps

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

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

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

$$\left(-m\right)^{2}n^{6}\left(-3m^{2}\right)^{3}$$

Calculate -m to the power of 2 and get m^{2}.

$$m^{2}n^{6}\left(-3m^{2}\right)^{3}$$

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

$$m^{2}n^{6}\left(-3\right)^{3}\left(m^{2}\right)^{3}$$

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

$$m^{2}n^{6}\left(-3\right)^{3}m^{6}$$

Calculate -3 to the power of 3 and get -27.

$$m^{2}n^{6}\left(-27\right)m^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$m^{8}n^{6}\left(-27\right)$$

Expand

$$-27n^{6}m^{8}$$

Solution Steps

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

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

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

$$\left(-m\right)^{2}n^{6}\left(-3m^{2}\right)^{3}$$

Calculate -m to the power of 2 and get m^{2}.

$$m^{2}n^{6}\left(-3m^{2}\right)^{3}$$

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

$$m^{2}n^{6}\left(-3\right)^{3}\left(m^{2}\right)^{3}$$

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

$$m^{2}n^{6}\left(-3\right)^{3}m^{6}$$

Calculate -3 to the power of 3 and get -27.

$$m^{2}n^{6}\left(-27\right)m^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$m^{8}n^{6}\left(-27\right)$$