Solve w^19/w^27

$$\frac { w ^ { 19 } } { w ^ { 27 } }$$

Evaluate

$$\frac{1}{w^{8}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{w^{19}}{w^{27}}$$

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

$$w^{19-27}$$

Subtract 27 from 19.

$$w^{-8}$$

Differentiate w.r.t. w

$$-\frac{8}{w^{9}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{1}{1}w^{19-27})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{-8})$$

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}.

$$-8w^{-8-1}$$

Do the arithmetic.

$$-8w^{-9}$$