Assessment And Learning In Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

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

7/4 4/49 49/4 1/4

Correct Answer:

4/49

Explanation:

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.

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