%5E-2-without-exponent.jpeg "(7/4)^-2 Without Exponent")
Understanding (7/4)^-2 without Exponents
The expression (7/4)^-2 might seem intimidating at first glance, but it's actually quite straightforward to understand. Let's break it down step by step:
Negative Exponent Rule
The key to understanding this expression lies in the rule of negative exponents. This rule states that any number raised to a negative exponent is equivalent to its reciprocal raised to the positive version of that exponent. In simpler terms:
x^-n = 1 / x^n
Applying the Rule
Let's apply this rule to our expression (7/4)^-2:
- Reciprocal: The reciprocal of (7/4) is (4/7).
- Positive Exponent: The positive version of -2 is 2.
Therefore, (7/4)^-2 is equivalent to (4/7)^2.
Final Calculation
Now we just need to calculate (4/7)^2:
(4/7)^2 = (4/7) * (4/7) = 16/49
Conclusion
So, (7/4)^-2 is equal to 16/49. By understanding the rule of negative exponents and following the steps, we were able to simplify the expression without using exponents.