Solve 30w^2x^3/48w^4x

$$\frac { 30 w ^ { 2 } x ^ { 3 } } { 48 w ^ { 4 } x }$$

Evaluate

$$\frac{5\times \left(\frac{x}{w}\right)^{2}}{8}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{30^{1}w^{2}x^{3}}{48^{1}w^{4}x^{1}}$$

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

$$\frac{30^{1}}{48^{1}}w^{2-4}x^{3-1}$$

Subtract 4 from 2.

$$\frac{30^{1}}{48^{1}}w^{-2}x^{3-1}$$

Subtract 1 from 3.

$$\frac{30^{1}}{48^{1}}\times \frac{1}{w^{2}}x^{2}$$

Reduce the fraction \frac{30}{48} to lowest terms by extracting and canceling out 6.

$$\frac{5}{8}\times \frac{1}{w^{2}}x^{2}$$

Differentiate w.r.t. x

$$\frac{5x}{4w^{2}}$$