Solve 4a^3*5adiv10a^4

$$4 a ^ { 3 } \times 5 a \div 10 a ^ { 4 }$$

Evaluate

$$2a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{4a^{4}\times 5}{10}a^{4}$$

Multiply 4 and 5 to get 20.

$$\frac{20a^{4}}{10}a^{4}$$

Divide 20a^{4} by 10 to get 2a^{4}.

$$2a^{4}a^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$2a^{8}$$

Differentiate w.r.t. a

$$16a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4a^{4}\times 5}{10}a^{4})$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{20a^{4}}{10}a^{4})$$

Divide 20a^{4} by 10 to get 2a^{4}.

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

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{8})$$

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

$$8\times 2a^{8-1}$$

Multiply 8 times 2.

$$16a^{8-1}$$

Subtract 1 from 8.

$$16a^{7}$$