Solve =405v^6y^7/75v^2y^3

$$= \frac { 405 v ^ { 6 } y ^ { 7 } } { 75 v ^ { 2 } y ^ { 3 } }$$

Evaluate

$$\frac{27\left(vy\right)^{4}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{405^{1}v^{6}y^{7}}{75^{1}v^{2}y^{3}}$$

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

$$\frac{405^{1}}{75^{1}}v^{6-2}y^{7-3}$$

Subtract 2 from 6.

$$\frac{405^{1}}{75^{1}}v^{4}y^{7-3}$$

Subtract 3 from 7.

$$\frac{405^{1}}{75^{1}}v^{4}y^{4}$$

Reduce the fraction \frac{405}{75} to lowest terms by extracting and canceling out 15.

$$\frac{27}{5}v^{4}y^{4}$$

Differentiate w.r.t. y

$$\frac{108y^{3}v^{4}}{5}$$