Solve frac{-3a^{-3}b^{-2}c^3}{-18a^4b^-5c^8}

$$\frac { - 3 a ^ { - 3 } b ^ { - 2 } c ^ { 3 } } { - 18 a ^ { 4 } b ^ { - 5 } c ^ { 8 } }$$

Evaluate

$$\frac{b^{3}}{6c^{5}a^{7}}$$

Solution Steps

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

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

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

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

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

$$\frac{-b^{3}}{-6c^{5}a^{7}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{b^{3}}{6c^{5}a^{7}}$$

Differentiate w.r.t. c

$$-\frac{5b^{3}}{6c^{6}a^{7}}$$