Solve a^3*8a^3*27a^3

$$a ^ { 3 } \cdot 8 a ^ { 3 } \cdot 27 a ^ { 3 }$$

Evaluate

$$216a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$a^{6}\times 8\times 27a^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$a^{9}\times 8\times 27$$

Multiply 8 and 27 to get 216.

$$a^{9}\times 216$$

Differentiate w.r.t. a

$$1944a^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}\times 8\times 27a^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}\times 8\times 27)$$

Multiply 8 and 27 to get 216.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}\times 216)$$

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

$$9\times 216a^{9-1}$$

Multiply 9 times 216.

$$1944a^{9-1}$$

Subtract 1 from 9.

$$1944a^{8}$$