Solve 5k^-1w^6*8kw^4

$$5 k ^ { - 1 } w ^ { 6 } \cdot 8 k w ^ { 4 }$$

Evaluate

$$40w^{10}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}\times \frac{1}{k}w^{6}\times 8^{1}k^{1}w^{4}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times 8^{1}\times \frac{1}{k}k^{1}w^{6}w^{4}$$

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

$$5^{1}\times 8^{1}k^{-1+1}w^{6+4}$$

Add the exponents -1 and 1.

$$5^{1}\times 8^{1}k^{0}w^{6+4}$$

For any number a except 0, a^{0}=1.

$$5^{1}\times 8^{1}w^{6+4}$$

Add the exponents 6 and 4.

$$5^{1}\times 8^{1}w^{10}$$

Multiply 5 times 8.

$$40w^{10}$$

Differentiate w.r.t. w

$$400w^{9}$$

Steps Using Definition of a Derivative

Multiply k^{-1} and k to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{6}\times 8w^{4})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{10}\times 8)$$

Multiply 5 and 8 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}w}(40w^{10})$$

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

$$10\times 40w^{10-1}$$

Multiply 10 times 40.

$$400w^{10-1}$$

Subtract 1 from 10.

$$400w^{9}$$