Solve r^{5}s^{-1}t^{0}*r^{2}s^{0}t^0*r^8s^0t^-5

$$r ^ { 5 } s ^ { - 1 } t ^ { 0 } \cdot r ^ { 2 } s ^ { 0 } t ^ { 0 } \cdot r ^ { 8 } s ^ { 0 } t ^ { - 5 }$$

Evaluate

$$\frac{r^{15}}{st^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$r^{7}s^{-1}t^{0}s^{0}t^{0}r^{8}s^{0}t^{-5}$$

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$r^{15}s^{-1}t^{0}s^{0}t^{0}s^{0}t^{-5}$$

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

$$r^{15}s^{-1}t^{0}t^{0}s^{0}t^{-5}$$

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

$$r^{15}s^{-1}t^{0}t^{0}t^{-5}$$

Multiply t^{0} and t^{0} to get 1.

$$r^{15}s^{-1}t^{-5}$$

Differentiate w.r.t. s

$$-\frac{r^{15}}{s^{2}t^{5}}$$