Solve frac{4a^{2}c^{4}}{3ab^{-2}c^2*4a^-1b^-4c^-3}

$$\frac { 4 a ^ { 2 } c ^ { 4 } } { 3 a b ^ { - 2 } c ^ { 2 } \cdot 4 a ^ { - 1 } b ^ { - 4 } c ^ { - 3 } }$$

Evaluate

$$\frac{a^{2}c^{5}b^{6}}{3}$$

Solution Steps

Multiply a and a^{-1} to get 1.

$$\frac{4a^{2}c^{4}}{3b^{-2}c^{2}\times 4b^{-4}c^{-3}}$$

To multiply powers of the same base, add their exponents. Add -2 and -4 to get -6.

$$\frac{4a^{2}c^{4}}{3b^{-6}c^{2}\times 4c^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{4a^{2}c^{4}}{3b^{-6}c^{-1}\times 4}$$

Cancel out 4 in both numerator and denominator.

$$\frac{a^{2}c^{4}}{3b^{-6}\times \frac{1}{c}}$$

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

$$\frac{a^{2}c^{5}}{3b^{-6}}$$

Differentiate w.r.t. c

$$\frac{5a^{2}c^{4}b^{6}}{3}$$