Solve m^12/m^3

$$\frac { m ^ { 12 } } { m ^ { 3 } }$$

Evaluate

$$m^{9}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{m^{12}}{m^{3}}$$

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

$$m^{12-3}$$

Subtract 3 from 12.

$$m^{9}$$

Differentiate w.r.t. m

$$9m^{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1}m^{12-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{9})$$

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}.

$$9m^{9-1}$$

Do the arithmetic.

$$9m^{8}$$