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

When simplifying (7/2)^-2, what is the new fraction after switching the fraction?

1. 7/2

2. 2/7

3. 14/4

4. 49/4

The correct answer is: 2/7

To simplify the expression \((7/2)^{-2}\), we apply the property of exponents that states that a negative exponent indicates the reciprocal of the base raised to the absolute value of that exponent. In this case, \((7/2)^{-2}\) means that we take the reciprocal of \(7/2\) and then square it. The reciprocal of \(7/2\) is \(2/7\). When we square that reciprocal, we get \((2/7)^{2} = 2^2 / 7^2 = 4/49\). However, the question specifically asks for the fraction after switching, not the final simplified result. Thus, after switching the fraction, \(7/2\) becomes \(2/7\). This is the correct new fraction following the rule for negative exponents and reflects the basic principle of taking the reciprocal. Therefore, the fraction \(2/7\) is indeed the new fraction derived from \((7/2)^{-2}\).