## Understanding (9/8)^-1 without exponents

The expression (9/8)^-1 might seem intimidating at first glance, especially if you're not comfortable with exponents. But fear not! We can rewrite this expression without using exponents and understand its meaning.

### The Rule of Negative Exponents

The key to understanding this expression lies in the rule of negative exponents: **a^-n = 1/a^n**. This rule states that any number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive version of the exponent.

### Applying the Rule to (9/8)^-1

Let's apply this rule to our expression:

(9/8)^-1 = 1/(9/8)^1

Now, any number raised to the power of 1 is simply itself. Therefore:

1/(9/8)^1 = 1/(9/8)

### Dividing by a Fraction

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 9/8 is 8/9.

Therefore:

1/(9/8) = 1 * (8/9) = **8/9**

### Conclusion

We have successfully rewritten (9/8)^-1 without using exponents and found its equivalent value to be 8/9. Understanding the rules of exponents is crucial for simplifying mathematical expressions and solving various problems.