Solve left(m^2nright)^2*mn^3+2m^5{n}^5

$${ \left( { m }^{ 2 } n \right) }^{ 2 } \times m { n }^{ 3 } +2 { m }^{ 5 } { n }^{ 5 }$$

Evaluate

$$3\left(mn\right)^{5}$$

Solution Steps

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

$$\left(m^{2}\right)^{2}n^{2}mn^{3}+2m^{5}n^{5}$$

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

$$m^{4}n^{2}mn^{3}+2m^{5}n^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$m^{5}n^{2}n^{3}+2m^{5}n^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$m^{5}n^{5}+2m^{5}n^{5}$$

Combine m^{5}n^{5} and 2m^{5}n^{5} to get 3m^{5}n^{5}.

$$3m^{5}n^{5}$$

Expand

$$3\left(mn\right)^{5}$$

Solution Steps

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

$$\left(m^{2}\right)^{2}n^{2}mn^{3}+2m^{5}n^{5}$$

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

$$m^{4}n^{2}mn^{3}+2m^{5}n^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$m^{5}n^{2}n^{3}+2m^{5}n^{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$m^{5}n^{5}+2m^{5}n^{5}$$

Combine m^{5}n^{5} and 2m^{5}n^{5} to get 3m^{5}n^{5}.

$$3m^{5}n^{5}$$