Solve b^-9*b^4*b^3

$$b ^ { - 9 } \cdot b ^ { 4 } \cdot b ^ { 3 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{-9}b^{4}b^{3}$$

Use the Multiplication Rule for Exponents.

$$b^{-9+4+3}$$

Add the exponents -9 and 4.

$$b^{-5+3}$$

Add the exponents -5 and 3.

$$b^{-2}$$

Differentiate w.r.t. b

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

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-5}b^{3})$$

To multiply powers of the same base, add their exponents. Add -5 and 3 to get -2.

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

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

$$-2b^{-2-1}$$

Subtract 1 from -2.

$$-2b^{-3}$$