Solve h^2divh^7=

$$h ^ { 2 } \div h ^ { 7 } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{h^{2}}{h^{7}}$$

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

$$h^{2-7}$$

Subtract 7 from 2.

$$h^{-5}$$

Differentiate w.r.t. h

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{1}{1}h^{2-7})$$

Do the arithmetic.

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

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}.

$$-5h^{-5-1}$$

Do the arithmetic.

$$-5h^{-6}$$