%5E-1.jpeg "(9/4)^-1")
Understanding (9/4)^-1
The expression (9/4)^-1 might seem intimidating at first, but it's actually quite simple to solve. Let's break down the concepts involved:
Understanding Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. In simpler terms:
x^-n = 1/x^n
Applying the Rule to (9/4)^-1
Using the rule above, we can rewrite (9/4)^-1 as:
(9/4)^-1 = 1 / (9/4)^1
Since any number raised to the power of 1 is itself, we have:
1 / (9/4)^1 = 1 / (9/4)
Dividing by a Fraction
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 9/4 is 4/9. Therefore:
1 / (9/4) = 1 * (4/9) = 4/9
Conclusion
Therefore, (9/4)^-1 is equal to 4/9.