Solve w*w^4*w^3

$$w \cdot w ^ { 4 } \cdot w ^ { 3 }$$

Evaluate

$$w^{8}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$w^{1}w^{4}w^{3}$$

Use the Multiplication Rule for Exponents.

$$w^{1+4+3}$$

Add the exponents 1 and 4.

$$w^{5+3}$$

Add the exponents 5 and 3.

$$w^{8}$$

Differentiate w.r.t. w

$$8w^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

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

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{8})$$

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

$$8w^{8-1}$$

Subtract 1 from 8.

$$8w^{7}$$