Question

If (-3) to the power of -5 equals 1/x, what is the value of x

Answer 1

`\bigodot\:\:-243`

Explanation:

• 
  `(-3)^(-5)=(1)/(x)` (Given)

• 
  `\implies (1)/( (-3)^(5))=(1)/(x)`

• 
  `\implies -(1)/(243)=(1)/(x)`

• 
  `\implies -243=x`

• 
  `\implies x = -243`

Answer 2

`\textsf{a)}\quad \sf -243`

Explanation:

`\textsf{Given equation}: \quad \sf (-3)^5=(1)/(x)`

`\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n)`

`\sf \implies (1)/((-3)^5)=(1)/(x)`

`\textsf{Apply exponent rule} \quad (-a)^(n)=-(a^n)\quad \textsf{if n is odd}`

`\implies \sf (1)/(-(3^5))=(1)/(x)`

`\implies \sf (1)/(-243)=(1)/(x)`

`\textsf{Therefore}, \sf x=-243`