Solve 12xy^2/5xy^10

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

Evaluate

$$\frac{12}{5y^{8}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 1.

$$\frac{12^{1}}{5^{1}}x^{0}y^{2-10}$$

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

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

Subtract 10 from 2.

$$\frac{12^{1}}{5^{1}}y^{-8}$$

Divide 12 by 5.

$$\frac{12}{5}\times \frac{1}{y^{8}}$$

Differentiate w.r.t. y

$$-\frac{96}{5y^{9}}$$