Solve frac{24a^{5}b^-7c^-4}{4a^-8c^6}

$$\frac { 24 a ^ { 5 } b ^ { - 7 } c ^ { - 4 } } { 4 a ^ { - 8 } c ^ { 6 } }$$

Evaluate

$$\frac{6a^{13}}{b^{7}c^{10}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{6b^{-7}c^{-4}a^{5}}{a^{-8}c^{6}}$$

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

$$\frac{6b^{-7}c^{-4}a^{13}}{c^{6}}$$

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

$$\frac{6b^{-7}a^{13}}{c^{10}}$$

Differentiate w.r.t. b

$$-\frac{42a^{13}}{b^{8}c^{10}}$$