Solve 12z^2y^3/15y^2z^7

$$\frac { 12 z ^ { 2 } y ^ { 3 } } { 15 y ^ { 2 } z ^ { 7 } }$$

Evaluate

$$\frac{4y}{5z^{5}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}z^{2}y^{3}}{15^{1}z^{7}y^{2}}$$

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

$$\frac{12^{1}}{15^{1}}z^{2-7}y^{3-2}$$

Subtract 7 from 2.

$$\frac{12^{1}}{15^{1}}z^{-5}y^{3-2}$$

Subtract 2 from 3.

$$\frac{12^{1}}{15^{1}}\times \frac{1}{z^{5}}y^{1}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}\times \frac{1}{z^{5}}y$$

Differentiate w.r.t. y

$$\frac{4}{5z^{5}}$$