Solve 2u^2v*(4uv^2)^2=

$$2 u ^ { 2 } v \cdot ( 4 u v ^ { 2 } ) ^ { 2 } =$$

Evaluate

$$32u^{4}v^{5}$$

Solution Steps

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

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

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

$$2u^{2}v\times 4^{2}u^{2}v^{4}$$

Calculate 4 to the power of 2 and get 16.

$$2u^{2}v\times 16u^{2}v^{4}$$

Multiply 2 and 16 to get 32.

$$32u^{2}vu^{2}v^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$32u^{4}vv^{4}$$

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

$$32u^{4}v^{5}$$

Expand

$$32u^{4}v^{5}$$

Solution Steps

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

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

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

$$2u^{2}v\times 4^{2}u^{2}v^{4}$$

Calculate 4 to the power of 2 and get 16.

$$2u^{2}v\times 16u^{2}v^{4}$$

Multiply 2 and 16 to get 32.

$$32u^{2}vu^{2}v^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$32u^{4}vv^{4}$$

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

$$32u^{4}v^{5}$$