Answer
$c^{4}$
Work Step by Step
Step 1: $(\frac{bc^{-2}}{bc^{-3}})^{4}$
Step 2: $\frac{(bc^{-2})^{4}}{(bc^{-3})^{4}}$
Step 3: $\frac{b^{4}(c^{-2})^{4}}{b^{4}(c^{-3})^{4}}$
Step 4: $\frac{b^{4}c^{-8}}{b^{4}c^{-12}}$
Step 5: Cancelling $b^{4}$ as it is common to both the numerator and the denominator, we get $\frac{c^{-8}}{c^{-12}}.$
Step 6: $\frac{c^{-8}}{c^{-12}}=c^{-8+12}=c^{4}$
