Solve h^8/h^17

$$\frac { h ^ { 8 } } { h ^ { 17 } }$$

Evaluate

$$\frac{1}{h^{9}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{h^{8}}{h^{17}}$$

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

$$h^{8-17}$$

Subtract 17 from 8.

$$h^{-9}$$

Differentiate w.r.t. h

$$-\frac{9}{h^{10}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{1}{1}h^{8-17})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(h^{-9})$$

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}.

$$-9h^{-9-1}$$

Do the arithmetic.

$$-9h^{-10}$$