%5E-2-without-exponents.jpeg "(3/7)^-2 Without Exponents")
Understanding (3/7)^-2
The expression (3/7)^-2 may seem confusing at first, but we can break it down and understand it without using exponents.
Reciprocals and Negative Exponents
The key to understanding this expression lies in understanding negative exponents. A negative exponent essentially indicates the reciprocal of the base raised to the positive version of that exponent.
In simpler terms: (a/b)^-n = (b/a)^n
Applying the Concept
Let's apply this to our example:
(3/7)^-2 = (7/3)^2
Now we've transformed the expression with a negative exponent into one with a positive exponent.
Calculating the Result
Finally, we can calculate the result:
(7/3)^2 = (7/3) * (7/3) = 49/9
Conclusion
Therefore, (3/7)^-2 is equivalent to 49/9. By understanding the concept of negative exponents and reciprocals, we can simplify expressions like this and arrive at the correct answer without relying on exponents.