Solve f^-8*f^4*f^6

$$f ^ { - 8 } \cdot f ^ { 4 } \cdot f ^ { 6 }$$

Evaluate

$$f^{2}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$f^{-8}f^{4}f^{6}$$

Use the Multiplication Rule for Exponents.

$$f^{-8+4+6}$$

Add the exponents -8 and 4.

$$f^{-4+6}$$

Add the exponents -4 and 6.

$$f^{2}$$

Differentiate w.r.t. f

$$2f$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -8 and 4 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{-4}f^{6})$$

To multiply powers of the same base, add their exponents. Add -4 and 6 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{2})$$

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

$$2f^{2-1}$$

Subtract 1 from 2.

$$2f^{1}$$

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

$$2f$$