Answer
$16a^{8}b^{26}c^{2 }$.
Work Step by Step
$\Rightarrow \left (\frac{ab^{-3}c^{-4}}{4a^5b^{10}c^{-3}} \right )^{-2}$
Simplify inside the parentheses. Subtract the exponents when dividing.
$\Rightarrow \left (2^{-2}a^{1-5}b^{-3-10}c^{-4+3} \right )^{-2}$
Simplify.
$\Rightarrow \left (2^{-2}a^{-4}b^{-13}c^{-1} \right )^{-2}$
Negative square each factor in parentheses.
$\Rightarrow (2^{-2})^{-2}(a^{-4})^{-2}(b^{-13})^{-2}(c^{-1} )^{-2}$
Multiply the exponents when raising a power to a power.
$\Rightarrow 2^{4}a^{8}b^{26}c^{2 }$
Simplify.
$\Rightarrow 16a^{8}b^{26}c^{2 }$.
