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

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

Evaluate

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

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 \frac{1}{8}.

$$\frac{c^{3}}{\frac{1}{8}d^{-6}}$$

Differentiate w.r.t. c

$$24c|c|d^{6}$$