Solve (c^frac{3{4}}*a^3)^-frac{1{2}}

$$( c ^ { \frac { 3 } { 4 } } \cdot a ^ { 3 } ) ^ { - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{1}{c^{\frac{3}{8}}a^{\frac{3}{2}}}$$

Solution Steps

Expand \left(c^{\frac{3}{4}}a^{3}\right)^{-\frac{1}{2}}.

$$\left(c^{\frac{3}{4}}\right)^{-\frac{1}{2}}\left(a^{3}\right)^{-\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -\frac{1}{2} to get -\frac{3}{8}.

$$c^{-\frac{3}{8}}\left(a^{3}\right)^{-\frac{1}{2}}$$

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

$$c^{-\frac{3}{8}}a^{-\frac{3}{2}}$$

Differentiate w.r.t. c

$$-\frac{3}{8c^{\frac{11}{8}}a^{\frac{3}{2}}}$$