Answer:
[tex]\textsf{a)}\quad \sf -243[/tex]
Step-by-step explanation:
[tex]\textsf{Given equation}: \quad \sf (-3)^5=\dfrac{1}{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\sf \implies \dfrac{1}{(-3)^5}=\dfrac{1}{x}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^{n}=-(a^n)\quad \textsf{if n is odd}[/tex]
[tex]\implies \sf \dfrac{1}{-(3^5)}=\dfrac{1}{x}[/tex]
[tex]\implies \sf \dfrac{1}{-243}=\dfrac{1}{x}[/tex]
[tex]\textsf{Therefore}, \sf x=-243[/tex]
