Problem

Fill in the box to make a true statement. \[ (5)^{\square}=\frac{1}{125} \]

Solution

Step 1 :The equation is asking for the exponent that when applied to 5 will result in 1/125.

Step 2 :This is equivalent to asking for the exponent that when applied to 5 will result in \(5^{-3}\), since 1/125 is the same as \(5^{-3}\).

Step 3 :Therefore, the exponent we are looking for is -3.

Step 4 :The exponent calculated is -3.0000000000000004, which is very close to -3. The slight difference is due to the precision limit of floating point numbers.

Step 5 :Therefore, we can conclude that the exponent is -3.

Step 6 :Final Answer: \(\boxed{-3}\)

From Solvely APP
Source: https://solvelyapp.com/problems/63CIIZKgEO/

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