Solve [3(m+m)^2]^2[-2(m+m)]^2

$$[ 3 ( m + m ) ^ { 2 } ] ^ { 2 } [ - 2 ( m + m ) ] ^ { 2 }$$

Evaluate

$$2304m^{6}$$

Solution Steps

Combine m and m to get 2m.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\left(12m^{2}\right)^{2}\left(-2\left(m+m\right)\right)^{2}$$

Expand \left(12m^{2}\right)^{2}.

$$12^{2}\left(m^{2}\right)^{2}\left(-2\left(m+m\right)\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$12^{2}m^{4}\left(-2\left(m+m\right)\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$144m^{4}\left(-2\left(m+m\right)\right)^{2}$$

Combine m and m to get 2m.

$$144m^{4}\left(-2\times 2m\right)^{2}$$

Multiply -2 and 2 to get -4.

$$144m^{4}\left(-4m\right)^{2}$$

Expand \left(-4m\right)^{2}.

$$144m^{4}\left(-4\right)^{2}m^{2}$$

Calculate -4 to the power of 2 and get 16.

$$144m^{4}\times 16m^{2}$$

Multiply 144 and 16 to get 2304.

$$2304m^{4}m^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$2304m^{6}$$

Expand

$$2304m^{6}$$

Solution Steps

Combine m and m to get 2m.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\left(12m^{2}\right)^{2}\left(-2\left(m+m\right)\right)^{2}$$

Expand \left(12m^{2}\right)^{2}.

$$12^{2}\left(m^{2}\right)^{2}\left(-2\left(m+m\right)\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$12^{2}m^{4}\left(-2\left(m+m\right)\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$144m^{4}\left(-2\left(m+m\right)\right)^{2}$$

Combine m and m to get 2m.

$$144m^{4}\left(-2\times 2m\right)^{2}$$

Multiply -2 and 2 to get -4.

$$144m^{4}\left(-4m\right)^{2}$$

Expand \left(-4m\right)^{2}.

$$144m^{4}\left(-4\right)^{2}m^{2}$$

Calculate -4 to the power of 2 and get 16.

$$144m^{4}\times 16m^{2}$$

Multiply 144 and 16 to get 2304.

$$2304m^{4}m^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$2304m^{6}$$