## Understanding (5/9)^-1

In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive value of the exponent. Let's break down (5/9)^-1:

### Reciprocal of a Fraction

- The
**reciprocal**of a fraction is found by flipping the numerator and denominator. So, the reciprocal of (5/9) is (9/5).

### Applying the Negative Exponent

- (5/9)^-1 is equivalent to 1 / (5/9)^1
- Since any number raised to the power of 1 is itself, this simplifies to 1 / (5/9)
- Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 1 / (5/9) is the same as 1 * (9/5)

### The Solution

**Therefore, (5/9)^-1 = 9/5**

This concept applies to any fraction raised to a negative exponent. By understanding the concept of reciprocals and negative exponents, you can easily solve these types of problems.