Solve (m^4)^-2*(m^3)^5

$$( m ^ { 4 } ) ^ { - 2 } \times ( m ^ { 3 } ) ^ { 5 }$$

Evaluate

$$m^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(m^{4}\right)^{-2}\left(m^{3}\right)^{5}$$

To raise a power to another power, multiply the exponents.

$$m^{4\left(-2\right)}m^{3\times 5}$$

Multiply 4 times -2.

$$m^{-8}m^{3\times 5}$$

Multiply 3 times 5.

$$m^{-8}m^{15}$$

To multiply powers of the same base, add their exponents.

$$m^{-8+15}$$

Add the exponents -8 and 15.

$$m^{7}$$

Differentiate w.r.t. m

$$7m^{6}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{-8}\left(m^{3}\right)^{5})$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{-8}m^{15})$$

To multiply powers of the same base, add their exponents. Add -8 and 15 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{7})$$

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

$$7m^{7-1}$$

Subtract 1 from 7.

$$7m^{6}$$