Solve frac{-36a^{7}b^{5}c^{3}}{40ab^{3}c^{2}}div27a^3b^5c^8/44abc^2

$$\frac { - 36 a ^ { 7 } b ^ { 5 } c ^ { 3 } } { 40 a b ^ { 3 } c ^ { 2 } } \div \frac { 27 a ^ { 3 } b ^ { 5 } c ^ { 8 } } { 44 a b c ^ { 2 } }$$

Evaluate

$$-\frac{22a^{4}}{15b^{2}c^{5}}$$

Solution Steps

Divide \frac{-36a^{7}b^{5}c^{3}}{40ab^{3}c^{2}} by \frac{27a^{3}b^{5}c^{8}}{44abc^{2}} by multiplying \frac{-36a^{7}b^{5}c^{3}}{40ab^{3}c^{2}} by the reciprocal of \frac{27a^{3}b^{5}c^{8}}{44abc^{2}}.

$$\frac{-36a^{7}b^{5}c^{3}\times 44abc^{2}}{40ab^{3}c^{2}\times 27a^{3}b^{5}c^{8}}$$

Cancel out 2\times 4\times 9abcb^{2}c^{2}c^{2}a^{3}b^{3} in both numerator and denominator.

$$\frac{-22aa^{3}}{3\times 5b^{2}c^{5}}$$

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

$$\frac{-22a^{4}}{3\times 5b^{2}c^{5}}$$

Multiply 3 and 5 to get 15.

$$\frac{-22a^{4}}{15b^{2}c^{5}}$$

Differentiate w.r.t. a

$$-\frac{88a^{3}}{15b^{2}c^{5}}$$