Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the final simplified form of (7/2)^-2?

1. 7/4

2. 4/49

3. 49/4

4. 1/4

The correct answer is: 4/49

To simplify \((\frac{7}{2})^{-2}\), we first need to understand how negative exponents work. A negative exponent indicates that we take the reciprocal of the base and then raise it to the positive of that exponent. So, \((\frac{7}{2})^{-2}\) can be rewritten as: \[ \left(\frac{2}{7}\right)^{2} \] Next, we square both the numerator and the denominator: \[ \frac{2^2}{7^2} = \frac{4}{49} \] Thus, the final simplified form of \((\frac{7}{2})^{-2}\) is indeed \(\frac{4}{49}\). This confirms that the option provided is correct. The steps illustrate how to properly handle negative exponents and simplify fractions.