Solve y^4/y^9

$$\frac { y ^ { 4 } } { y ^ { 9 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{4}}{y^{9}}$$

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

$$y^{4-9}$$

Subtract 9 from 4.

$$y^{-5}$$

Differentiate w.r.t. y

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{4-9})$$

Do the arithmetic.

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

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}.

$$-5y^{-5-1}$$

Do the arithmetic.

$$-5y^{-6}$$