Solve 48v^10x^5/18v^2x^2

$$\frac { 48 v ^ { 10 } x ^ { 5 } } { 18 v ^ { 2 } x ^ { 2 } }$$

Evaluate

$$\frac{8x^{3}v^{8}}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{48^{1}v^{10}x^{5}}{18^{1}v^{2}x^{2}}$$

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

$$\frac{48^{1}}{18^{1}}v^{10-2}x^{5-2}$$

Subtract 2 from 10.

$$\frac{48^{1}}{18^{1}}v^{8}x^{5-2}$$

Subtract 2 from 5.

$$\frac{48^{1}}{18^{1}}v^{8}x^{3}$$

Reduce the fraction \frac{48}{18} to lowest terms by extracting and canceling out 6.

$$\frac{8}{3}v^{8}x^{3}$$

Differentiate w.r.t. x

$$8x^{2}v^{8}$$