Solve 18a^7*5a^-5

$$18 a ^ { 7 } \times 5 a ^ { - 5 }$$

Evaluate

$$90a^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$18a^{2}\times 5$$

Multiply 18 and 5 to get 90.

$$90a^{2}$$

Differentiate w.r.t. a

$$180a$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and -5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(18a^{2}\times 5)$$

Multiply 18 and 5 to get 90.

$$\frac{\mathrm{d}}{\mathrm{d}a}(90a^{2})$$

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

$$2\times 90a^{2-1}$$

Multiply 2 times 90.

$$180a^{2-1}$$

Subtract 1 from 2.

$$180a^{1}$$

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

$$180a$$