%5E-1-without-exponent.jpeg "(9/4)^-1 Without Exponent")
Understanding (9/4)^-1 Without Exponents
The expression (9/4)^-1 might look intimidating at first glance, but it's actually quite simple to understand once we break it down. Let's explore how to rewrite this expression without using exponents.
The Magic of Negative Exponents
The key to understanding this expression lies in the concept of negative exponents. A negative exponent essentially means "take the reciprocal" of the base.
In simpler terms:
- (9/4)^-1 is the same as 1 / (9/4)
Reciprocals in Action
Now, we know that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of (9/4) is (4/9).
Therefore:
- (9/4)^-1 = 1 / (9/4) = 1 * (4/9) = 4/9
Conclusion
We successfully rewrote (9/4)^-1 without using exponents. The result is simply 4/9. This exercise highlights the power of understanding negative exponents and reciprocals to simplify complex mathematical expressions.