We can rewrite the equation \( 5^x = \frac{1}{25} \) to solve for \(x\).

### Step-by-step solution:
1. Recognize that \( \frac{1}{25} \) is the same as \( 5^{-2} \), because \( 25 = 5^2 \), and the reciprocal of a number raised to a power is equivalent to the negative exponent of that number.

   So, we rewrite the equation as:
   \[
   5^x = 5^{-2}
   \]

2. Since the bases are the same (both are base 5), we can set the exponents equal to each other:
   \[
   x = -2
   \]

Thus, the solution is \( x = -2 \).

Do you want more details or have any questions?

Here are 5 related questions:
1. What is the general rule for solving exponential equations with the same base?
2. How can you express \( \frac{1}{a^n} \) in terms of negative exponents?
3. If \( 5^x = 25 \), what is the value of \(x\)?
4. What is the relationship between exponents and logarithms in solving exponential equations?
5. How do you solve equations where the exponents are variables, like \( 5^{2x} = 125 \)?

**Tip:** Always try to express numbers as powers of the same base when solving exponential equations.

Learn how to solve the exponential equation 5^x = 1/25. This step-by-step guide explains the key concepts of negative exponents and how to solve for x when the equation involves the same base. Suitable for students in Grades 8-10.

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