Solve (5m^{3}n^{2})^2(2mn^4p^0)^3

$$( 5 m ^ { 3 } n ^ { 2 } ) ^ { 2 } ( 2 m n ^ { 4 } p ^ { 0 } ) ^ { 3 }$$

Evaluate

$$200m^{9}n^{16}$$

Solution Steps

Expand \left(5m^{3}n^{2}\right)^{2}.

$$5^{2}\left(m^{3}\right)^{2}\left(n^{2}\right)^{2}\times \left(2mn^{4}p^{0}\right)^{3}$$

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

$$5^{2}m^{6}\left(n^{2}\right)^{2}\times \left(2mn^{4}p^{0}\right)^{3}$$

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

$$5^{2}m^{6}n^{4}\times \left(2mn^{4}p^{0}\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$25m^{6}n^{4}\times \left(2mn^{4}p^{0}\right)^{3}$$

Calculate p to the power of 0 and get 1.

$$25m^{6}n^{4}\times \left(2mn^{4}\times 1\right)^{3}$$

Multiply 2 and 1 to get 2.

$$25m^{6}n^{4}\times \left(2mn^{4}\right)^{3}$$

Expand \left(2mn^{4}\right)^{3}.

$$25m^{6}n^{4}\times 2^{3}m^{3}\left(n^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$25m^{6}n^{4}\times 2^{3}m^{3}n^{12}$$

Calculate 2 to the power of 3 and get 8.

$$25m^{6}n^{4}\times 8m^{3}n^{12}$$

Multiply 25 and 8 to get 200.

$$200m^{6}n^{4}m^{3}n^{12}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$200m^{9}n^{4}n^{12}$$

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$200m^{9}n^{16}$$

Expand

$$200m^{9}n^{16}$$

Solution Steps

Expand \left(5m^{3}n^{2}\right)^{2}.

$$5^{2}\left(m^{3}\right)^{2}\left(n^{2}\right)^{2}\times \left(2mn^{4}p^{0}\right)^{3}$$

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

$$5^{2}m^{6}\left(n^{2}\right)^{2}\times \left(2mn^{4}p^{0}\right)^{3}$$

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

$$5^{2}m^{6}n^{4}\times \left(2mn^{4}p^{0}\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$25m^{6}n^{4}\times \left(2mn^{4}p^{0}\right)^{3}$$

Calculate p to the power of 0 and get 1.

$$25m^{6}n^{4}\times \left(2mn^{4}\times 1\right)^{3}$$

Multiply 2 and 1 to get 2.

$$25m^{6}n^{4}\times \left(2mn^{4}\right)^{3}$$

Expand \left(2mn^{4}\right)^{3}.

$$25m^{6}n^{4}\times 2^{3}m^{3}\left(n^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$25m^{6}n^{4}\times 2^{3}m^{3}n^{12}$$

Calculate 2 to the power of 3 and get 8.

$$25m^{6}n^{4}\times 8m^{3}n^{12}$$

Multiply 25 and 8 to get 200.

$$200m^{6}n^{4}m^{3}n^{12}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$200m^{9}n^{4}n^{12}$$

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$200m^{9}n^{16}$$