Solve 10x^5y^2/12y^7x^5

$$\frac { 10 x ^ { 5 } y ^ { 2 } } { 12 y ^ { 7 } x ^ { 5 } }$$

Evaluate

$$\frac{5}{6y^{5}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}x^{5}y^{2}}{12^{1}x^{5}y^{7}}$$

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

$$\frac{10^{1}}{12^{1}}x^{5-5}y^{2-7}$$

Subtract 5 from 5.

$$\frac{10^{1}}{12^{1}}x^{0}y^{2-7}$$

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

$$\frac{10^{1}}{12^{1}}y^{2-7}$$

Subtract 7 from 2.

$$\frac{10^{1}}{12^{1}}y^{-5}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}\times \frac{1}{y^{5}}$$

Differentiate w.r.t. y

$$-\frac{25}{6y^{6}}$$