Solve 4a^5b^0/12a^12

$$\frac { 4 a ^ { 5 } b ^ { 0 } } { 12 a ^ { 12 } }$$

Evaluate

$$\frac{1}{3a^{7}}$$

Solution Steps

Cancel out 4a^{5} in both numerator and denominator.

$$\frac{b^{0}}{3a^{7}}$$

Calculate b to the power of 0 and get 1.

$$\frac{1}{3a^{7}}$$

Differentiate w.r.t. a

$$-\frac{7}{3a^{8}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4b^{0}}{12}a^{5-12})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{3}a^{-7})$$

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}.

$$-7\times \frac{1}{3}a^{-7-1}$$

Do the arithmetic.

$$-\frac{7}{3}a^{-8}$$