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

What does (-2) in the exponent represent in the expression (7/2)^-2?

1. The exponent is positive

2. The fraction should be inverted

3. The fraction should be squared

4. The operation should never be performed

The correct answer is: The fraction should be inverted

In the expression \((7/2)^{-2}\), the negative exponent indicates that the base \(7/2\) should be inverted. When you have a negative exponent, the rule is that you take the reciprocal of the base and make the exponent positive. Thus, \((7/2)^{-2}\) can be rewritten as \(1/(7/2)^2\). Next, applying the exponent to the inverted base, \((7/2)^2\) means squaring both the numerator and the denominator, resulting in \((7^2)/(2^2) = 49/4\). Therefore, the negative exponent effectively translates the expression into a form that involves inverting the fraction and changing the sign of the exponent to positive. This demonstrates how negative exponents operate and reinforces the rule regarding the handling of exponents in arithmetic.