Solve (y^{2})^{3}(s^4)^2(y^2)^3

$$( y ^ { 2 } ) ^ { 3 } ( s ^ { 4 } ) ^ { 2 } ( y ^ { 2 } ) ^ { 3 }$$

Evaluate

$$s^{8}y^{12}$$

Solution Steps

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

$$y^{6}\left(s^{4}\right)^{2}\left(y^{2}\right)^{3}$$

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

$$y^{6}s^{8}\left(y^{2}\right)^{3}$$

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

$$y^{6}s^{8}y^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$y^{12}s^{8}$$

Differentiate w.r.t. s

$$8s^{7}y^{12}$$