Solve frac{4{a}^frac{2{3}}{b}^-frac{3{3}}}{-2/3{a}^-frac{3{3}}{b}^frac{2{3}}}

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

Evaluate

$$-6\times \left(\frac{a}{b}\right)^{\frac{5}{3}}$$

Short Solution Steps

Divide 3 by 3 to get 1.

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

Divide 3 by 3 to get 1.

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

Factor the expressions that are not already factored.

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

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

$$\frac{4\times \frac{1}{b}a^{\frac{5}{3}}}{-\frac{2}{3}b^{\frac{2}{3}}}$$

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

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

Differentiate w.r.t. b

$$\frac{10a^{\frac{5}{3}}}{b^{\frac{8}{3}}}$$