Question

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Answer 1

`\text{C. }1`

Explanation:

In the question, we're given that the notation
`\#\#(a,b,c)` produces a number
`a` less than the product of
`b` and
`c` raised to the
`a` power. Let the number produced be
`n`. As a mathematical equation, we can write this production as
`n=(bc)^a-a`

For
`\#\#(2, 5, x)`, we can assign:

• 
  `a\implies 2`
• 
  `b\implies 5`
• 
  `c\implies x`

Substituting these values into
`n=(bc)^a-a`, we get:

`23=(5x)^2-2`

Add 2 to both sides:

`25=(5x)^2`

Take the square root of both sides:

`5=|5x|`

For
`y=|z|`, there are two cases:

`\begin{cases}y=z,\\y=-z\end{cases}`

Therefore, we have:

`\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}`

The only answer choice applicable is
`\boxed{\text{C. }1}`.