Solve (m^2n)^2(2mn^5)^4

$$( m ^ { 2 } n ) ^ { 2 } ( 2 m n ^ { 5 } ) ^ { 4 }$$

Evaluate

$$16m^{8}n^{22}$$

Solution Steps

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

$$\left(m^{2}\right)^{2}n^{2}\times \left(2mn^{5}\right)^{4}$$

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

$$m^{4}n^{2}\times \left(2mn^{5}\right)^{4}$$

Expand \left(2mn^{5}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$m^{4}n^{2}\times 2^{4}m^{4}n^{20}$$

Calculate 2 to the power of 4 and get 16.

$$m^{4}n^{2}\times 16m^{4}n^{20}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$m^{8}n^{2}\times 16n^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$m^{8}n^{22}\times 16$$

Expand

$$16m^{8}n^{22}$$

Solution Steps

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

$$\left(m^{2}\right)^{2}n^{2}\times \left(2mn^{5}\right)^{4}$$

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

$$m^{4}n^{2}\times \left(2mn^{5}\right)^{4}$$

Expand \left(2mn^{5}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$m^{4}n^{2}\times 2^{4}m^{4}n^{20}$$

Calculate 2 to the power of 4 and get 16.

$$m^{4}n^{2}\times 16m^{4}n^{20}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$m^{8}n^{2}\times 16n^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$m^{8}n^{22}\times 16$$