Solve (a^-frac{2{3}}b^frac{2{3}})^frac{3{2}}

$$( a ^ { - \frac { 2 } { 3 } } b ^ { \frac { 2 } { 3 } } ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{|b|}{|a|}$$

Solution Steps

Expand \left(a^{-\frac{2}{3}}b^{\frac{2}{3}}\right)^{\frac{3}{2}}.

$$\left(a^{-\frac{2}{3}}\right)^{\frac{3}{2}}\left(b^{\frac{2}{3}}\right)^{\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and \frac{3}{2} to get -1.

$$a^{-1}\left(b^{\frac{2}{3}}\right)^{\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and \frac{3}{2} to get 1.

$$a^{-1}b^{1}$$

Calculate b to the power of 1 and get b.

$$a^{-1}b$$

Differentiate w.r.t. b

$$\frac{sign(b)}{|a|}$$