Solve (4^2a^2)*(6^3a^2)

$$( 4 ^ { 2 } a ^ { 2 } ) \times ( 6 ^ { 3 } a ^ { 2 } )$$

Evaluate

$$3456a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$4^{2}a^{4}\times 6^{3}$$

Calculate 4 to the power of 2 and get 16.

$$16a^{4}\times 6^{3}$$

Calculate 6 to the power of 3 and get 216.

$$16a^{4}\times 216$$

Multiply 16 and 216 to get 3456.

$$3456a^{4}$$

Differentiate w.r.t. a

$$13824a^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4^{2}a^{4}\times 6^{3})$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a^{4}\times 6^{3})$$

Calculate 6 to the power of 3 and get 216.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a^{4}\times 216)$$

Multiply 16 and 216 to get 3456.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3456a^{4})$$

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

$$4\times 3456a^{4-1}$$

Multiply 4 times 3456.

$$13824a^{4-1}$$

Subtract 1 from 4.

$$13824a^{3}$$