Solve 64a^2*5a^3*3a^5

$$64 a ^ { 2 } \times 5 a ^ { 3 } \times 3 a ^ { 5 }$$

Evaluate

$$960a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$64a^{5}\times 5\times 3a^{5}$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$64a^{10}\times 5\times 3$$

Multiply 64 and 5 to get 320.

$$320a^{10}\times 3$$

Multiply 320 and 3 to get 960.

$$960a^{10}$$

Differentiate w.r.t. a

$$9600a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(64a^{5}\times 5\times 3a^{5})$$

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(64a^{10}\times 5\times 3)$$

Multiply 64 and 5 to get 320.

$$\frac{\mathrm{d}}{\mathrm{d}a}(320a^{10}\times 3)$$

Multiply 320 and 3 to get 960.

$$\frac{\mathrm{d}}{\mathrm{d}a}(960a^{10})$$

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

$$10\times 960a^{10-1}$$

Multiply 10 times 960.

$$9600a^{10-1}$$

Subtract 1 from 10.

$$9600a^{9}$$