Solve frac{m^frac{3{2}}*m^frac{5{2}}}{m^3}

$$\frac { m ^ { \frac { 3 } { 2 } } \times m ^ { \frac { 5 } { 2 } } } { m ^ { 3 } }$$

Evaluate

$$m$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{5}{2} to get 4.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$m^{1}$$

Calculate m to the power of 1 and get m.

$$m$$

Differentiate w.r.t. m

$$1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{5}{2} to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{4}}{m^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

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

Calculate m to the power of 1 and get m.

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

The derivative of ax^{n} is nax^{n-1}.

$$m^{1-1}$$

Subtract 1 from 1.

$$m^{0}$$

For any term t except 0, t^{0}=1.

$$1$$