Solve (3uv^2)(6u^2v^3)^2=

$$( 3 u v ^ { 2 } ) ( 6 u ^ { 2 } v ^ { 3 } ) ^ { 2 } =$$

Evaluate

$$108u^{5}v^{8}$$

Solution Steps

Expand \left(6u^{2}v^{3}\right)^{2}.

$$3uv^{2}\times 6^{2}\left(u^{2}\right)^{2}\left(v^{3}\right)^{2}$$

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

$$3uv^{2}\times 6^{2}u^{4}\left(v^{3}\right)^{2}$$

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

$$3uv^{2}\times 6^{2}u^{4}v^{6}$$

Calculate 6 to the power of 2 and get 36.

$$3uv^{2}\times 36u^{4}v^{6}$$

Multiply 3 and 36 to get 108.

$$108uv^{2}u^{4}v^{6}$$

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

$$108u^{5}v^{2}v^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$108u^{5}v^{8}$$

Expand

$$108u^{5}v^{8}$$

Solution Steps

Expand \left(6u^{2}v^{3}\right)^{2}.

$$3uv^{2}\times 6^{2}\left(u^{2}\right)^{2}\left(v^{3}\right)^{2}$$

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

$$3uv^{2}\times 6^{2}u^{4}\left(v^{3}\right)^{2}$$

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

$$3uv^{2}\times 6^{2}u^{4}v^{6}$$

Calculate 6 to the power of 2 and get 36.

$$3uv^{2}\times 36u^{4}v^{6}$$

Multiply 3 and 36 to get 108.

$$108uv^{2}u^{4}v^{6}$$

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

$$108u^{5}v^{2}v^{6}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$108u^{5}v^{8}$$