Solve 9m^{4}(n^{2})^3+(-3m^2n^3)^2

$$9 m ^ { 4 } ( n ^ { 2 } ) ^ { 3 } + ( - 3 m ^ { 2 } n ^ { 3 } ) ^ { 2 }$$

Evaluate

$$18m^{4}n^{6}$$

Solution Steps

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

$$9m^{4}n^{6}+\left(-3m^{2}n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}m^{4}\left(n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}m^{4}n^{6}$$

Calculate -3 to the power of 2 and get 9.

$$9m^{4}n^{6}+9m^{4}n^{6}$$

Combine 9m^{4}n^{6} and 9m^{4}n^{6} to get 18m^{4}n^{6}.

$$18m^{4}n^{6}$$

Expand

$$18m^{4}n^{6}$$

Solution Steps

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

$$9m^{4}n^{6}+\left(-3m^{2}n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}m^{4}\left(n^{3}\right)^{2}$$

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

$$9m^{4}n^{6}+\left(-3\right)^{2}m^{4}n^{6}$$

Calculate -3 to the power of 2 and get 9.

$$9m^{4}n^{6}+9m^{4}n^{6}$$

Combine 9m^{4}n^{6} and 9m^{4}n^{6} to get 18m^{4}n^{6}.

$$18m^{4}n^{6}$$