Solve m^3/m^8

$$\frac{ { m }^{ 3 } }{ { m }^{ 8 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{m^{3}}{m^{8}}$$

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

$$m^{3-8}$$

Subtract 8 from 3.

$$m^{-5}$$

Differentiate w.r.t. m

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1}m^{3-8})$$

Do the arithmetic.

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

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}.

$$-5m^{-5-1}$$

Do the arithmetic.

$$-5m^{-6}$$