Solve m:m^4=

$$m : m ^ { 4 } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$m^{1-4}$$

Subtract 4 from 1.

$$m^{-3}$$

Differentiate w.r.t. m

$$-\frac{3}{m^{4}}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$-3m^{-3-1}$$

Do the arithmetic.

$$-3m^{-4}$$