Solve a^{2}bc^5:[(-2b^3c^2):(b^3c)]

$$a ^ { 2 } b c ^ { 5 } : [ ( - 2 b ^ { 3 } c ^ { 2 } ) : ( b ^ { 3 } c ) ]$$

Evaluate

$$-\frac{ba^{2}c^{4}}{2}$$

Solution Steps

Divide a^{2}bc^{5} by \frac{-2b^{3}c^{2}}{b^{3}c} by multiplying a^{2}bc^{5} by the reciprocal of \frac{-2b^{3}c^{2}}{b^{3}c}.

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

Cancel out bb^{2}c^{2} in both numerator and denominator.

$$\frac{bca^{2}c^{3}}{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{bc^{4}a^{2}}{-2}$$

Differentiate w.r.t. b

$$-\frac{a^{2}c^{4}}{2}$$