Solve m^2/m^8

$$\frac { m ^ { 2 } } { m ^ { 8 } }$$

Evaluate

$$\frac{1}{m^{6}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{m^{2}}{m^{8}}$$

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

$$m^{2-8}$$

Subtract 8 from 2.

$$m^{-6}$$

Differentiate w.r.t. m

$$-\frac{6}{m^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1}m^{2-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{-6})$$

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}.

$$-6m^{-6-1}$$

Do the arithmetic.

$$-6m^{-7}$$