Solve s^{3}t^{-9}u^{0}v^{-1}*s^{0}t^{-1}u^{7}v*s^0t^9u^0v^-8

$$s ^ { 3 } t ^ { - 9 } u ^ { 0 } v ^ { - 1 } \cdot s ^ { 0 } t ^ { - 1 } u ^ { 7 } v \cdot s ^ { 0 } t ^ { 9 } u ^ { 0 } v ^ { - 8 }$$

Evaluate

$$\frac{s^{3}u^{7}}{tv^{8}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$s^{3}t^{-9}u^{0}v^{-1}t^{-1}u^{7}vs^{0}t^{9}u^{0}v^{-8}$$

To multiply powers of the same base, add their exponents. Add 3 and 0 to get 3.

$$s^{3}t^{-9}u^{0}v^{-1}t^{-1}u^{7}vt^{9}u^{0}v^{-8}$$

To multiply powers of the same base, add their exponents. Add -9 and -1 to get -10.

$$s^{3}t^{-10}u^{0}v^{-1}u^{7}vt^{9}u^{0}v^{-8}$$

To multiply powers of the same base, add their exponents. Add -10 and 9 to get -1.

$$s^{3}t^{-1}u^{0}v^{-1}u^{7}vu^{0}v^{-8}$$

To multiply powers of the same base, add their exponents. Add 0 and 7 to get 7.

$$s^{3}t^{-1}u^{7}v^{-1}vu^{0}v^{-8}$$

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$s^{3}t^{-1}u^{7}v^{-1}vv^{-8}$$

Multiply v^{-1} and v to get 1.

$$s^{3}t^{-1}u^{7}v^{-8}$$

Differentiate w.r.t. s

$$\frac{3s^{2}u^{7}}{tv^{8}}$$