Question

Find x, where x^6 = 9^-3 and x > 0.

x > 0


bit rusty with exponents so could I have some help?

Answer 1

`~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^6~~ = ~~9^(-3)\implies x^6~~ = ~~(3^2)^(-3)\implies x^6~~ = ~~3^(-6) \\\\\\ x^6~~ = ~~(3^(-1))^6\implies x=3^(-1)\implies x=\cfrac{1}{3^1}\implies x=\cfrac{1}{3}`