Solve 6a^3*6a^-2

$$6 a ^ { 3 } \cdot 6 a ^ { - 2 }$$

Evaluate

$$36a$$

Solution Steps

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

$$6a^{1}\times 6$$

Calculate a to the power of 1 and get a.

$$6a\times 6$$

Multiply 6 and 6 to get 36.

$$36a$$

Differentiate w.r.t. a

$$36$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{1}\times 6)$$

Calculate a to the power of 1 and get a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a\times 6)$$

Multiply 6 and 6 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}a}(36a)$$

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

$$36a^{1-1}$$

Subtract 1 from 1.

$$36a^{0}$$

For any term t except 0, t^{0}=1.

$$36\times 1$$

For any term t, t\times 1=t and 1t=t.

$$36$$