Question

Find the value of the following expression:

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (2^8\cdot 3^{-5}\cdot 6^0)^{-2}\cdot \left( \cfrac{3^{-2}}{2^3} \right)^4\cdot 2^{28}\implies \stackrel{\textit{distributing the exponent}}{(2^{8\cdot -2}\cdot 3^{-5\cdot -2}\cdot 6^{0\cdot -2})\cdot \left( \cfrac{3^{-2\cdot 4}}{2^{3\cdot 4}} \right)\cdot 2^{28}}$

$\bf (2^{-16}\cdot 3^{10}\cdot 6^0)\cdot \left( \cfrac{3^{-8}}{2^{12}} \right)\cdot 2^{28}\implies (2^{-16}\cdot 3^{10}\cdot 1)\cdot ( 3^{-8}\cdot 2^{-12})\cdot 2^{28} \\\\\\ 2^{-16}\cdot 2^{-12}\cdot 2^{28}\cdot 3^{10}\cdot 3^{-8}\implies 2^{-16-12+28}\cdot 3^{10-8}\implies 2^{0}\cdot 3^{2} \\\\\\ 1\cdot 9\implies 9$