Solve -27a^7b^-6/18a^-2b^2=

$$\frac { - 27 a ^ { 7 } b ^ { - 6 } } { 18 a ^ { - 2 } b ^ { 2 } } =$$

Evaluate

$$-\frac{3a^{9}}{2b^{8}}$$

Solution Steps

Cancel out 9 in both numerator and denominator.

$$\frac{-3b^{-6}a^{7}}{2a^{-2}b^{2}}$$

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

$$\frac{-3b^{-6}a^{9}}{2b^{2}}$$

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

$$\frac{-3a^{9}}{2b^{8}}$$

Differentiate w.r.t. a

$$-\frac{27\times \left(\frac{a}{b}\right)^{8}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{\frac{27}{b^{6}}}{18b^{2}}\right)a^{7-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{3}{2b^{8}}\right)a^{9})$$

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}.

$$9\left(-\frac{3}{2b^{8}}\right)a^{9-1}$$

Do the arithmetic.

$$\left(-\frac{27}{2b^{8}}\right)a^{8}$$