Solve t^{-8}u^{-1}v^{0}*t^{-4}u^{-3}v^9*t^-4u^-4v^-4

$$t ^ { - 8 } u ^ { - 1 } v ^ { 0 } \cdot t ^ { - 4 } u ^ { - 3 } v ^ { 9 } \cdot t ^ { - 4 } u ^ { - 4 } v ^ { - 4 }$$

Evaluate

$$\frac{v^{5}}{u^{8}t^{16}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -8 and -4 to get -12.

$$t^{-12}u^{-1}v^{0}u^{-3}v^{9}t^{-4}u^{-4}v^{-4}$$

To multiply powers of the same base, add their exponents. Add -12 and -4 to get -16.

$$t^{-16}u^{-1}v^{0}u^{-3}v^{9}u^{-4}v^{-4}$$

To multiply powers of the same base, add their exponents. Add -1 and -3 to get -4.

$$t^{-16}u^{-4}v^{0}v^{9}u^{-4}v^{-4}$$

To multiply powers of the same base, add their exponents. Add -4 and -4 to get -8.

$$t^{-16}u^{-8}v^{0}v^{9}v^{-4}$$

To multiply powers of the same base, add their exponents. Add 0 and 9 to get 9.

$$t^{-16}u^{-8}v^{9}v^{-4}$$

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

$$t^{-16}u^{-8}v^{5}$$

Differentiate w.r.t. t

$$-\frac{16v^{5}}{u^{8}t^{17}}$$