Solve [(2^{2}m^3n^4)^2]^3=

$$[ ( 2 ^ { 2 } m ^ { 3 } n ^ { 4 } ) ^ { 2 } ] ^ { 3 } =$$

Evaluate

$$4096m^{18}n^{24}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Expand \left(4m^{3}n^{4}\right)^{2}.

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

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

$$\left(4^{2}m^{6}\left(n^{4}\right)^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(4^{2}m^{6}n^{8}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$\left(16m^{6}n^{8}\right)^{3}$$

Expand \left(16m^{6}n^{8}\right)^{3}.

$$16^{3}\left(m^{6}\right)^{3}\left(n^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$16^{3}m^{18}\left(n^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$16^{3}m^{18}n^{24}$$

Calculate 16 to the power of 3 and get 4096.

$$4096m^{18}n^{24}$$

Expand

$$4096m^{18}n^{24}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Expand \left(4m^{3}n^{4}\right)^{2}.

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

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

$$\left(4^{2}m^{6}\left(n^{4}\right)^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(4^{2}m^{6}n^{8}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$\left(16m^{6}n^{8}\right)^{3}$$

Expand \left(16m^{6}n^{8}\right)^{3}.

$$16^{3}\left(m^{6}\right)^{3}\left(n^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$16^{3}m^{18}\left(n^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$16^{3}m^{18}n^{24}$$

Calculate 16 to the power of 3 and get 4096.

$$4096m^{18}n^{24}$$