Solve (s^{2})^3*5(r^0)^3*rs^2

$$( s ^ { 2 } ) ^ { 3 } \times 5 ( r ^ { 0 } ) ^ { 3 } \times r s ^ { 2 }$$

Evaluate

$$5rs^{8}$$

Solution Steps

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

$$s^{6}\times 5\left(r^{0}\right)^{3}rs^{2}$$

To raise a power to another power, multiply the exponents. Multiply 0 and 3 to get 0.

$$s^{6}\times 5r^{0}rs^{2}$$

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

$$s^{8}\times 5r^{0}r$$

To multiply powers of the same base, add their exponents. Add 0 and 1 to get 1.

$$s^{8}\times 5r^{1}$$

Calculate r to the power of 1 and get r.

$$s^{8}\times 5r$$

Differentiate w.r.t. r

$$5s^{8}$$