Solve (w^{2})^{2}(p^2)^5(w^2)^5

$$( w ^ { 2 } ) ^ { 2 } ( p ^ { 2 } ) ^ { 5 } ( w ^ { 2 } ) ^ { 5 }$$

Evaluate

$$p^{10}w^{14}$$

Solution Steps

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

$$w^{4}\left(p^{2}\right)^{5}\left(w^{2}\right)^{5}$$

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

$$w^{4}p^{10}\left(w^{2}\right)^{5}$$

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

$$w^{4}p^{10}w^{10}$$

To multiply powers of the same base, add their exponents. Add 4 and 10 to get 14.

$$w^{14}p^{10}$$

Differentiate w.r.t. p

$$10p^{9}w^{14}$$