Solve 3/4a^7b^3cdiv2/3a^5b^2c=

$$\frac { 3 } { 4 } a ^ { 7 } b ^ { 3 } c \div \frac { 2 } { 3 } a ^ { 5 } b ^ { 2 } c =$$

Evaluate

$$\frac{9c^{2}b^{5}a^{12}}{8}$$

Solution Steps

Divide \frac{3}{4}a^{7}b^{3}c by \frac{2}{3} by multiplying \frac{3}{4}a^{7}b^{3}c by the reciprocal of \frac{2}{3}.

$$\frac{\frac{3}{4}a^{7}b^{3}c\times 3}{2}a^{5}b^{2}c$$

Multiply \frac{3}{4} and 3 to get \frac{9}{4}.

$$\frac{\frac{9}{4}a^{7}b^{3}c}{2}a^{5}b^{2}c$$

Divide \frac{9}{4}a^{7}b^{3}c by 2 to get \frac{9}{8}a^{7}b^{3}c.

$$\frac{9}{8}a^{7}b^{3}ca^{5}b^{2}c$$

To multiply powers of the same base, add their exponents. Add 7 and 5 to get 12.

$$\frac{9}{8}a^{12}b^{3}cb^{2}c$$

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

$$\frac{9}{8}a^{12}b^{5}cc$$

Multiply c and c to get c^{2}.

$$\frac{9}{8}a^{12}b^{5}c^{2}$$

Differentiate w.r.t. a

$$\frac{27c^{2}b^{5}a^{11}}{2}$$