Solve 4a*a*5a*a

$$4 a \times a \times 5 a \times a$$

Evaluate

$$20a^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$4^{1}a^{1}a^{1}\times 5^{1}a^{1}a^{1}$$

Use the Commutative Property of Multiplication.

$$4^{1}\times 5^{1}a^{1}a^{1}a^{1}a^{1}$$

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

$$4^{1}\times 5^{1}a^{1+1}a^{1+1}$$

Add the exponents 1 and 1.

$$4^{1}\times 5^{1}a^{2}a^{1+1}$$

Add the exponents 1 and 1.

$$4^{1}\times 5^{1}a^{2}a^{2}$$

Multiply 4 times 5.

$$20a^{2}a^{2}$$

Differentiate w.r.t. a

$$80a^{3}$$

Steps Using Definition of a Derivative

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{2}\times 5aa)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{3}\times 5a)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{4}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20a^{4})$$

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

$$4\times 20a^{4-1}$$

Multiply 4 times 20.

$$80a^{4-1}$$

Subtract 1 from 4.

$$80a^{3}$$