Question

Simplify the following expression. 4 to -11/3 power ÷ 4 to -2/3 power

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}\\\\ 4^{-(11)/(3)}/ 4^{-(2)/(3)}\implies \cfrac{4^{-(11)/(3)}}{4^{-(2)/(3)}}\implies 4^{-(11)/(3)}\cdot 4^{(2)/(3)}\implies 4^{-(11)/(3)+(2)/(3)} \\\\\\ 4^{-(9)/(3)}\implies 4^(-3)\implies \cfrac{1}{4^3}\implies \cfrac{1}{64}`