Solve (p^{4}w^2)(u^2w^4)^4

$$( p ^ { 4 } w ^ { 2 } ) ( u ^ { 2 } w ^ { 4 } ) ^ { 4 }$$

Evaluate

$$p^{4}u^{8}w^{18}$$

Solution Steps

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

$$p^{4}w^{2}\left(u^{2}\right)^{4}\left(w^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$p^{4}w^{2}u^{8}\left(w^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$p^{4}w^{2}u^{8}w^{16}$$

To multiply powers of the same base, add their exponents. Add 2 and 16 to get 18.

$$p^{4}w^{18}u^{8}$$

Expand

$$p^{4}u^{8}w^{18}$$

Solution Steps

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

$$p^{4}w^{2}\left(u^{2}\right)^{4}\left(w^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$p^{4}w^{2}u^{8}\left(w^{4}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$p^{4}w^{2}u^{8}w^{16}$$

To multiply powers of the same base, add their exponents. Add 2 and 16 to get 18.

$$p^{4}w^{18}u^{8}$$