Question

What value of n solves the equation 2^n =1/8

Answer 1

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ 2^n=\cfrac{1}{8}\qquad \boxed{8=2^3}\qquad 2^n=\cfrac{1}{2^3}\implies 2^n=2^{-3} \\\\\\ \textit{the base is the same, the exponents must also be the same}\quad n=-3$