Solve 24t^6r^2/8t^3r^5

$$\frac { 24 t ^ { 6 } r ^ { 2 } } { 8 t ^ { 3 } r ^ { 5 } }$$

Evaluate

$$3\times \left(\frac{t}{r}\right)^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{24^{1}t^{6}r^{2}}{8^{1}t^{3}r^{5}}$$

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

$$\frac{24^{1}}{8^{1}}t^{6-3}r^{2-5}$$

Subtract 3 from 6.

$$\frac{24^{1}}{8^{1}}t^{3}r^{2-5}$$

Subtract 5 from 2.

$$\frac{24^{1}}{8^{1}}t^{3}r^{-3}$$

Divide 24 by 8.

$$3t^{3}\times \frac{1}{r^{3}}$$

Differentiate w.r.t. r

$$-\frac{9t^{3}}{r^{4}}$$