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

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

Evaluate

$$41472n^{13}m^{17}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(9mn^{5}\right)^{2}\times \left(2^{3}m^{5}n\right)^{3}$$

Expand \left(9mn^{5}\right)^{2}.

$$9^{2}m^{2}\left(n^{5}\right)^{2}\times \left(2^{3}m^{5}n\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$9^{2}m^{2}n^{10}\times \left(2^{3}m^{5}n\right)^{3}$$

Calculate 9 to the power of 2 and get 81.

$$81m^{2}n^{10}\times \left(2^{3}m^{5}n\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$81m^{2}n^{10}\times \left(8m^{5}n\right)^{3}$$

Expand \left(8m^{5}n\right)^{3}.

$$81m^{2}n^{10}\times 8^{3}\left(m^{5}\right)^{3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$81m^{2}n^{10}\times 8^{3}m^{15}n^{3}$$

Calculate 8 to the power of 3 and get 512.

$$81m^{2}n^{10}\times 512m^{15}n^{3}$$

Multiply 81 and 512 to get 41472.

$$41472m^{2}n^{10}m^{15}n^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 15 to get 17.

$$41472m^{17}n^{10}n^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$41472m^{17}n^{13}$$

Expand

$$41472n^{13}m^{17}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(9mn^{5}\right)^{2}\times \left(2^{3}m^{5}n\right)^{3}$$

Expand \left(9mn^{5}\right)^{2}.

$$9^{2}m^{2}\left(n^{5}\right)^{2}\times \left(2^{3}m^{5}n\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$9^{2}m^{2}n^{10}\times \left(2^{3}m^{5}n\right)^{3}$$

Calculate 9 to the power of 2 and get 81.

$$81m^{2}n^{10}\times \left(2^{3}m^{5}n\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$81m^{2}n^{10}\times \left(8m^{5}n\right)^{3}$$

Expand \left(8m^{5}n\right)^{3}.

$$81m^{2}n^{10}\times 8^{3}\left(m^{5}\right)^{3}n^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$81m^{2}n^{10}\times 8^{3}m^{15}n^{3}$$

Calculate 8 to the power of 3 and get 512.

$$81m^{2}n^{10}\times 512m^{15}n^{3}$$

Multiply 81 and 512 to get 41472.

$$41472m^{2}n^{10}m^{15}n^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 15 to get 17.

$$41472m^{17}n^{10}n^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$41472m^{17}n^{13}$$