Solve (6r^{5})(5^3t^2)(12r^4t^3)

$$( 6 r ^ { 5 } ) ( 5 ^ { 3 } t ^ { 2 } ) ( 12 r ^ { 4 } t ^ { 3 } )$$

Evaluate

$$9000t^{5}r^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$6r^{9}\times 5^{3}t^{2}\times 12t^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$6r^{9}\times 5^{3}t^{5}\times 12$$

Calculate 5 to the power of 3 and get 125.

$$6r^{9}\times 125t^{5}\times 12$$

Multiply 6 and 125 to get 750.

$$750r^{9}t^{5}\times 12$$

Multiply 750 and 12 to get 9000.

$$9000r^{9}t^{5}$$

Differentiate w.r.t. r

$$81000t^{5}r^{8}$$