Answer
$\dfrac{1}{2^{12}}$
Work Step by Step
$8^{-3} \cdot 32 \div 16^2
\\=(2^3)^{-3} \cdot 2^5 \div (2^4)^2$
Use the power rule $(a^m)^n=a^{mn}$ to obtain:
$=2^{3(-3)} \cdot 2^5 \div 2^{4(2)}
\\=2^{-9} \cdot 2^5 \div 2^8$
Use the rule $a^m \cdot a^n = a^{m+n}$ to obtain:
$=2^{-9+5} \div 2^8
\\=2^{-4} \div 2^8$
Use the rule $a^m \div a^n = a^{m-n}$ to obtain:
$=2^{-4-8}
\\=2^{-12}$
Use the negative exponent rule ($a^{-m} =\frac{1}{a^m}, a\ne 0$) to obtain:
$=\dfrac{1}{2^{12}}$