Solve 24r^{10}s^{13}div18r^15s^8*27r^4s^6

$$24 r ^ { 10 } s ^ { 13 } \div 18 r ^ { 15 } s ^ { 8 } \times 27 r ^ { 4 } s ^ { 6 }$$

Evaluate

$$36s^{27}r^{29}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 15 and 4 to get 19.

$$\frac{24r^{10}s^{13}}{18}r^{19}s^{8}\times 27s^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$\frac{24r^{10}s^{13}}{18}r^{19}s^{14}\times 27$$

Divide 24r^{10}s^{13} by 18 to get \frac{4}{3}r^{10}s^{13}.

$$\frac{4}{3}r^{10}s^{13}r^{19}s^{14}\times 27$$

To multiply powers of the same base, add their exponents. Add 10 and 19 to get 29.

$$\frac{4}{3}r^{29}s^{13}s^{14}\times 27$$

To multiply powers of the same base, add their exponents. Add 13 and 14 to get 27.

$$\frac{4}{3}r^{29}s^{27}\times 27$$

Multiply \frac{4}{3} and 27 to get 36.

$$36r^{29}s^{27}$$

Differentiate w.r.t. r

$$1044s^{27}r^{28}$$