Solve 8t^10u^3/2t^2u^9

$$\frac { 8 t ^ { 10 } u ^ { 3 } } { 2 t ^ { 2 } u ^ { 9 } }$$

Evaluate

$$\frac{4t^{8}}{u^{6}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}t^{10}u^{3}}{2^{1}t^{2}u^{9}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{8^{1}}{2^{1}}t^{10-2}u^{3-9}$$

Subtract 2 from 10.

$$\frac{8^{1}}{2^{1}}t^{8}u^{3-9}$$

Subtract 9 from 3.

$$\frac{8^{1}}{2^{1}}t^{8}u^{-6}$$

Divide 8 by 2.

$$4t^{8}\times \frac{1}{u^{6}}$$

Differentiate w.r.t. u

$$-\frac{24t^{8}}{u^{7}}$$