Solve frac{2a^{6}b^-3c^3}{3a^-3b^6}

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

Evaluate

$$\frac{2\times \left(\frac{a}{b}\right)^{9}c^{3}}{3}$$

Solution Steps

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

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

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

$$\frac{2c^{3}a^{9}}{3b^{9}}$$

Differentiate w.r.t. c

$$2\times \left(\frac{a}{b}\right)^{9}c^{2}$$