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

Which of the following steps is NOT part of simplifying the expression (7/2)^-2?

1. Converting the negative exponent to a positive

2. Inverting the fraction

3. Multiplying the fraction by itself

4. Adding 2 to both numerator and denominator

The correct answer is: Adding 2 to both numerator and denominator

When simplifying the expression \( \left( \frac{7}{2} \right)^{-2} \), one begins by addressing the negative exponent. The negative exponent indicates that the base should be inverted and then raised to the positive version of that exponent. Specifically, \( a^{-n} \) is equivalent to \( \frac{1}{a^n} \). So, for \( \left( \frac{7}{2} \right)^{-2} \), the first step involves converting the negative exponent to a positive exponent by inverting the fraction: 1. Invert \( \frac{7}{2} \) to get \( \frac{2}{7} \). 2. Raise this result to the power of 2. Next, you would multiply \( \frac{2}{7} \) by itself: 3. This step is expressed as \( \left( \frac{2}{7} \right)^2 = \frac{2^2}{7^2} = \frac{4}{49} \). However, adding 2 to both the numerator and denominator is not a part of the simplification process for this expression. It does not relate to the operations needed to