Solve (-4mn)^3*(-2m^2)^3

$$( - 4 m n ) ^ { 3 } \cdot ( - 2 m ^ { 2 } ) ^ { 3 }$$

Evaluate

$$512n^{3}m^{9}$$

Solution Steps

Expand \left(-4mn\right)^{3}.

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

Calculate -4 to the power of 3 and get -64.

$$-64m^{3}n^{3}\left(-2m^{2}\right)^{3}$$

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

$$-64m^{3}n^{3}\left(-2\right)^{3}\left(m^{2}\right)^{3}$$

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

$$-64m^{3}n^{3}\left(-2\right)^{3}m^{6}$$

Calculate -2 to the power of 3 and get -8.

$$-64m^{3}n^{3}\left(-8\right)m^{6}$$

Multiply -64 and -8 to get 512.

$$512m^{3}n^{3}m^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$512m^{9}n^{3}$$

Expand

$$512n^{3}m^{9}$$

Solution Steps

Expand \left(-4mn\right)^{3}.

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

Calculate -4 to the power of 3 and get -64.

$$-64m^{3}n^{3}\left(-2m^{2}\right)^{3}$$

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

$$-64m^{3}n^{3}\left(-2\right)^{3}\left(m^{2}\right)^{3}$$

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

$$-64m^{3}n^{3}\left(-2\right)^{3}m^{6}$$

Calculate -2 to the power of 3 and get -8.

$$-64m^{3}n^{3}\left(-8\right)m^{6}$$

Multiply -64 and -8 to get 512.

$$512m^{3}n^{3}m^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$512m^{9}n^{3}$$