Solve 18m^4/2m=

$$\frac { 18 m ^ { 4 } } { 2 m } =$$

Evaluate

$$9m^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}m^{4}}{2^{1}m^{1}}$$

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

$$\frac{18^{1}m^{4-1}}{2^{1}}$$

Subtract 1 from 4.

$$\frac{18^{1}m^{3}}{2^{1}}$$

Divide 18 by 2.

$$9m^{3}$$

Differentiate w.r.t. m

$$27m^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{18}{2}m^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(9m^{3})$$

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}.

$$3\times 9m^{3-1}$$

Do the arithmetic.

$$27m^{2}$$