Solve (m^{4}n^{6})^2+(-m)^8*(n^3)^4

$$( m ^ { 4 } n ^ { 6 } ) ^ { 2 } + ( - m ) ^ { 8 } \cdot ( n ^ { 3 } ) ^ { 4 }$$

Evaluate

$$2m^{8}n^{12}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(m^{4}n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

Expand \left(m^{4}n^{6}\right)^{2}.

$$\left(m^{4}\right)^{2}\left(n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

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

$$m^{8}\left(n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$m^{8}n^{12}+\left(-m\right)^{8}n^{12}$$

Expand \left(-m\right)^{8}.

$$m^{8}n^{12}+\left(-1\right)^{8}m^{8}n^{12}$$

Calculate -1 to the power of 8 and get 1.

$$m^{8}n^{12}+1m^{8}n^{12}$$

Combine m^{8}n^{12} and 1m^{8}n^{12} to get 2m^{8}n^{12}.

$$2m^{8}n^{12}$$

Expand

$$2m^{8}n^{12}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(m^{4}n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

Expand \left(m^{4}n^{6}\right)^{2}.

$$\left(m^{4}\right)^{2}\left(n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

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

$$m^{8}\left(n^{6}\right)^{2}+\left(-m\right)^{8}n^{12}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$m^{8}n^{12}+\left(-m\right)^{8}n^{12}$$

Expand \left(-m\right)^{8}.

$$m^{8}n^{12}+\left(-1\right)^{8}m^{8}n^{12}$$

Calculate -1 to the power of 8 and get 1.

$$m^{8}n^{12}+1m^{8}n^{12}$$

Combine m^{8}n^{12} and 1m^{8}n^{12} to get 2m^{8}n^{12}.

$$2m^{8}n^{12}$$