Solve k^3*k^-6*k^-4

$$k ^ { 3 } \cdot k ^ { - 6 } \cdot k ^ { - 4 }$$

Evaluate

$$\frac{1}{k^{7}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$k^{3}k^{-6}k^{-4}$$

Use the Multiplication Rule for Exponents.

$$k^{3-6-4}$$

Add the exponents 3 and -6.

$$k^{-3-4}$$

Add the exponents -3 and -4.

$$k^{-7}$$

Differentiate w.r.t. k

$$-\frac{7}{k^{8}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

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

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{-7})$$

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

$$-7k^{-7-1}$$

Subtract 1 from -7.

$$-7k^{-8}$$