Solve 2a^-2b^-3/-12a^3b^-5

$$\frac{ 2 { a }^{ -2 } { b }^{ -3 } }{ -12 { a }^{ 3 } { b }^{ -5 } }$$

Evaluate

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

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Differentiate w.r.t. b

$$-\frac{b}{3a^{5}}$$