Solve a*3^5*3^2

$$a \cdot 3 ^ { 5 } \times 3 ^ { 2 }$$

Evaluate

$$2187a$$

Solution Steps

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

$$a\times 3^{7}$$

Calculate 3 to the power of 7 and get 2187.

$$a\times 2187$$

Differentiate w.r.t. a

$$2187$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 3^{7})$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 2187)$$

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

$$2187a^{1-1}$$

Subtract 1 from 1.

$$2187a^{0}$$

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

$$2187\times 1$$

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

$$2187$$