Solve (c^-4/16d^8)^frac{3{4}}

$$( \frac { c ^ { - 4 } } { 16 d ^ { 8 } } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$\frac{1}{8\left(|c|\right)^{3}d^{6}}$$

Solution Steps

To raise \frac{c^{-4}}{16d^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(c^{-4}\right)^{\frac{3}{4}}}{\left(16d^{8}\right)^{\frac{3}{4}}}$$

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

$$\frac{c^{-3}}{\left(16d^{8}\right)^{\frac{3}{4}}}$$

Expand \left(16d^{8}\right)^{\frac{3}{4}}.

$$\frac{c^{-3}}{16^{\frac{3}{4}}\left(d^{8}\right)^{\frac{3}{4}}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and \frac{3}{4} to get 6.

$$\frac{c^{-3}}{16^{\frac{3}{4}}d^{6}}$$

Calculate 16 to the power of \frac{3}{4} and get 8.

$$\frac{c^{-3}}{8d^{6}}$$

Differentiate w.r.t. c

$$-\frac{3|c|}{8c^{5}d^{6}}$$