Solve 9r^2s^3/5(2r^2s/3)(45rs^2/2)

$$\frac { 9 r ^ { 2 } s ^ { 3 } } { 5 } ( \frac { 2 r ^ { 2 } s } { 3 } ) ( \frac { 45 r s ^ { 2 } } { 2 } )$$

Evaluate

$$27r^{5}s^{6}$$

Solution Steps

Multiply \frac{9r^{2}s^{3}}{5} times \frac{2r^{2}s}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9r^{2}s^{3}\times 2r^{2}s}{5\times 3}\times \frac{45rs^{2}}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\times 3sr^{2}r^{2}s^{3}}{5}\times \frac{45rs^{2}}{2}$$

Multiply \frac{2\times 3sr^{2}r^{2}s^{3}}{5} times \frac{45rs^{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3sr^{2}r^{2}s^{3}\times 45rs^{2}}{5\times 2}$$

Cancel out 2\times 5 in both numerator and denominator.

$$3\times 9rsr^{2}r^{2}s^{2}s^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3\times 9r^{3}sr^{2}s^{2}s^{3}$$

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

$$3\times 9r^{5}ss^{2}s^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3\times 9r^{5}s^{3}s^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$3\times 9r^{5}s^{6}$$

Multiply 3 and 9 to get 27.

$$27r^{5}s^{6}$$

Differentiate w.r.t. r

$$135r^{4}s^{6}$$