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

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

Solution Steps

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

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

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

$$m^{4}n^{2}\left(-m\right)n^{3}+2m^{5}n^{5}$$

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

$$m^{4}n^{5}\left(-m\right)+2m^{5}n^{5}$$

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

$$m^{5}n^{5}\left(-1\right)+2m^{5}n^{5}$$

Combine m^{5}n^{5}\left(-1\right) and 2m^{5}n^{5} to get m^{5}n^{5}.

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

Expand

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

Solution Steps

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

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

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

$$m^{4}n^{2}\left(-m\right)n^{3}+2m^{5}n^{5}$$

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

$$m^{4}n^{5}\left(-m\right)+2m^{5}n^{5}$$

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

$$m^{5}n^{5}\left(-1\right)+2m^{5}n^{5}$$

Combine m^{5}n^{5}\left(-1\right) and 2m^{5}n^{5} to get m^{5}n^{5}.

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