Solve (a)^3*3^3*3^4

$$( a ) ^ { 3 } \cdot 3 ^ { 3 } \cdot 3 ^ { 4 }$$

Evaluate

$$2187a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

Calculate 3 to the power of 7 and get 2187.

$$a^{3}\times 2187$$

Differentiate w.r.t. a

$$6561a^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

Calculate 3 to the power of 7 and get 2187.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}\times 2187)$$

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

$$3\times 2187a^{3-1}$$

Multiply 3 times 2187.

$$6561a^{3-1}$$

Subtract 1 from 3.

$$6561a^{2}$$