Solve y^5/y^7=

$$\frac { y ^ { 5 } } { y ^ { 7 } } =$$

Evaluate

$$\frac{1}{y^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{5}}{y^{7}}$$

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

$$y^{5-7}$$

Subtract 7 from 5.

$$y^{-2}$$

Differentiate w.r.t. y

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{5-7})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-2y^{-2-1}$$

Do the arithmetic.

$$-2y^{-3}$$