Solve (9x^2y/30x^2y^2)

$$( \frac { 9 x ^ { 2 } y } { 30 x ^ { 2 } y ^ { 2 } } )$$

Evaluate

$$\frac{3}{10y}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}x^{2}y^{1}}{30^{1}x^{2}y^{2}}$$

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

$$\frac{9^{1}}{30^{1}}x^{2-2}y^{1-2}$$

Subtract 2 from 2.

$$\frac{9^{1}}{30^{1}}x^{0}y^{1-2}$$

For any number a except 0, a^{0}=1.

$$\frac{9^{1}}{30^{1}}y^{1-2}$$

Subtract 2 from 1.

$$\frac{9^{1}}{30^{1}}\times \frac{1}{y}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{3}{10}\times \frac{1}{y}$$

Differentiate w.r.t. y

$$-\frac{3}{10y^{2}}$$