%5E-2-without-exponents.jpeg "(5/7)^-2 Without Exponents")
Understanding (5/7)^-2 without Exponents
The expression (5/7)^-2 might look intimidating, but we can break it down to understand it without using exponents.
What does a negative exponent mean?
A negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. In other words:
x^-n = 1 / x^n
Applying this to our problem
In our case, we have (5/7)^-2. Using the rule above, we can rewrite it as:
(5/7)^-2 = 1 / (5/7)^2
Calculating the square
Now, we need to calculate (5/7)^2. This means multiplying the fraction by itself:
(5/7) * (5/7) = 25/49
Completing the calculation
Substituting this back into our expression, we have:
1 / (5/7)^2 = 1 / (25/49)
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 25/49 is 49/25. Therefore:
1 / (25/49) = 1 * (49/25) = 49/25
Conclusion
Therefore, (5/7)^-2 is equivalent to 49/25, which can be expressed as a fraction or a decimal (1.96).