%5E-2-without-exponents.jpeg "(9/7)^-2 Without Exponents")
Understanding (9/7)^-2 without Exponents
The expression (9/7)^-2 might look intimidating at first glance, but it's actually quite straightforward once you understand the rules of exponents. Let's break it down:
Negative Exponents
A negative exponent means we take the reciprocal of the base raised to the positive version of the exponent. In our case:
(9/7)^-2 = 1 / (9/7)^2
Fractions to a Power
Now we have to deal with (9/7)^2. Raising a fraction to a power means we raise both the numerator and denominator to that power:
(9/7)^2 = 9^2 / 7^2
Calculating the Squares
Finally, we calculate the squares:
9^2 = 9 * 9 = 81 7^2 = 7 * 7 = 49
Putting it all Together
Now we can substitute everything back into our original expression:
(9/7)^-2 = 1 / (9/7)^2 = 1 / (9^2 / 7^2) = 1 / (81/49)
Since dividing by a fraction is the same as multiplying by its reciprocal:
1 / (81/49) = 1 * (49/81) = 49/81
Therefore, (9/7)^-2 is equivalent to 49/81 without using exponents.