Solve 4a^5/8a^3*2a

$$\frac { 4 a ^ { 5 } } { 8 a ^ { 3 } \times 2 a }$$

Evaluate

$$\frac{a}{4}$$

Solution Steps

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

$$\frac{4a^{5}}{8a^{4}\times 2}$$

Cancel out 4a^{4} in both numerator and denominator.

$$\frac{a}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{a}{4}$$

Differentiate w.r.t. a

$$\frac{1}{4} = 0.25$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{16a}a^{5-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4a}a^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{1}{4a}a^{2-1}$$

Do the arithmetic.

$$\frac{1}{2a}a^{1}$$

For any term t, t^{1}=t.

$$\frac{1}{2a}a$$