Solve 1m^10/m^5=

$$1 \frac { m ^ { 10 } } { m ^ { 5 } } =$$

Evaluate

$$m^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{m^{10}}{m^{5}}$$

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

$$m^{10-5}$$

Subtract 5 from 10.

$$m^{5}$$

Differentiate w.r.t. m

$$5m^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{1}m^{10-5})$$

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.

$$5m^{4}$$