Solve m^5*(m^-3)^3*m^2

$$m ^ { 5 } \times ( m ^ { - 3 } ) ^ { 3 } \times m ^ { 2 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$m^{5}m^{-9}m^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and -9 to get -4.

$$m^{-4}m^{2}$$

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

$$m^{-2}$$

Differentiate w.r.t. m

$$-\frac{2}{m^{3}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{5}m^{-9}m^{2})$$

To multiply powers of the same base, add their exponents. Add 5 and -9 to get -4.

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

To multiply powers of the same base, add their exponents. Add -4 and 2 to get -2.

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

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

$$-2m^{-2-1}$$

Subtract 1 from -2.

$$-2m^{-3}$$