Solve frac{-6a^-3b^frac{3{4}}}{15a^-2b^frac{1{3}}}

$$\frac { - 6 a ^ { - 3 } b ^ { \frac { 3 } { 4 } } } { 15 a ^ { - 2 } b ^ { \frac { 1 } { 3 } } }$$

Evaluate

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

Solution Steps

Cancel out 3\sqrt[3]{b} in both numerator and denominator.

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

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

$$\frac{-2b^{\frac{5}{12}}}{5a^{1}}$$

Calculate a to the power of 1 and get a.

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

Differentiate w.r.t. b

$$-\frac{1}{6b^{\frac{7}{12}}a}$$