It looks like you are asking how to simplify the expression \( \frac{0.28^x}{0.28^{x-1}} \).

To simplify this expression, follow these steps:

1. **Recognize the laws of exponents:** The expression \( \frac{a^m}{a^n} = a^{m-n} \), where \( a \) is the base, and \( m \) and \( n \) are the exponents.

2. **Apply this law to the given expression:**

\[
\frac{0.28^x}{0.28^{x-1}} = 0.28^{x-(x-1)}
\]

3. **Simplify the exponent:**

\[
x - (x - 1) = x - x + 1 = 1
\]

4. **Thus, the expression simplifies to:**

\[
0.28^1 = 0.28
\]

So, the simplified form of \( \frac{0.28^x}{0.28^{x-1}} \) is **0.28**.

Would you like more details or have any other questions?

Here are some related questions for further exploration:
1. How would the expression change if the base was \( b \) instead of 0.28?
2. What if the expression were \( \frac{b^{2x}}{b^x} \)?
3. How does the expression behave when the exponent in the denominator is \( x+1 \) instead of \( x-1 \)?
4. What is the significance of simplifying expressions like these in solving exponential equations?
5. How does the property of exponents apply to other mathematical operations?
6. What happens when the base is a variable instead of a constant?
7. How would you differentiate the function \( f(x) = \frac{0.28^x}{0.28^{x-1}} \)?
8. Can you generalize the result for any base \( a \)?

**Tip:** Familiarize yourself with the laws of exponents—they are fundamental in simplifying algebraic expressions and solving equations, particularly in exponential and logarithmic contexts.

Learn how to simplify the exponential expression 0.28^x/(0.28^(x-1)) step-by-step. Understand the laws of exponents and their application in simplifying algebraic expressions. Suitable for high school students and anyone studying exponential functions.

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