We are given the equation:

\[
4^{-x} = 0.25
\]

We can express \(0.25\) as a fraction with base 4. Notice that \(0.25 = \frac{1}{4}\), which can be rewritten as \(4^{-1}\). Therefore, we have:

\[
4^{-x} = 4^{-1}
\]

Since the bases are the same, we can equate the exponents:

\[
-x = -1
\]

Solving for \(x\):

\[
x = 1
\]

Thus, the solution is \(x = 1\).

Would you like more details or have any questions?

Here are five related questions for further practice:

1. Solve \(3^{-x} = \frac{1}{9}\).
2. Solve \(5^{-x} = 0.2\).
3. Solve \(2^{-x} = \frac{1}{8}\).
4. Solve \(7^{-x} = \frac{1}{49}\).
5. Solve \(9^{-x} = 0.01\).

**Tip:** Always try to express both sides of the equation with the same base when solving exponential equations.

Learn how to solve the exponential equation 4^-x = 0.25 with a clear, step-by-step solution. This problem covers essential algebraic concepts, including exponent rules and equal bases property. Ideal for students in Grades 8-10.

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