Solve h^9/h^11

$$\frac { h ^ { 9 } } { h ^ { 11 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{h^{9}}{h^{11}}$$

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

$$h^{9-11}$$

Subtract 11 from 9.

$$h^{-2}$$

Differentiate w.r.t. h

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{1}{1}h^{9-11})$$

Do the arithmetic.

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

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}.

$$-2h^{-2-1}$$

Do the arithmetic.

$$-2h^{-3}$$