Solve frac{a^{3}*c^{3}*c^6*a^2}{c^4*a^2*c*a}=

$$\frac { a ^ { 3 } \cdot c ^ { 3 } \cdot c ^ { 6 } \cdot a ^ { 2 } } { c ^ { 4 } \cdot a ^ { 2 } \cdot c \cdot a } =$$

Evaluate

$$a^{2}c^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{a^{5}c^{9}}{c^{4}a^{2}ca}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{a^{5}c^{9}}{c^{5}a^{2}a}$$

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

$$\frac{a^{5}c^{9}}{c^{5}a^{3}}$$

Cancel out a^{3}c^{5} in both numerator and denominator.

$$a^{2}c^{4}$$

Differentiate w.r.t. c

$$4a^{2}c^{3}$$