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

What is the first step in solving the expression (7/2)^-2?

1. Convert the fraction to a positive exponent

2. Multiply both numerator and denominator by -1

3. Switch the fraction to make the exponent positive

4. Apply the exponent directly to the numerator

The correct answer is: Switch the fraction to make the exponent positive

To solve the expression \((7/2)^{-2}\), the first step is indeed to switch the fraction to make the exponent positive. When an exponent is negative, it indicates the reciprocal of the base raised to the positive exponent. Hence, for a negative exponent, the rule is: \[ a^{-n} = \frac{1}{a^n} \] Applying this rule to the fraction \((7/2)^{-2}\) means you take the reciprocal of \((7/2)\) to convert the exponent from negative to positive. This takes the form: \[ (7/2)^{-2} = \frac{1}{(7/2)^2} \] Thus, the equivalent expression has a positive exponent, which allows you to proceed to further calculations easily. Other options do not align with this mathematical principle. Simply converting the fraction to a positive exponent directly or multiplying both the numerator and denominator by -1 does not correctly transform the expression according to the rules of exponents. Applying the exponent directly to the numerator without addressing the negative sign would lead you to a misunderstanding of how exponents function with fractions. Therefore, switching the fraction to a positive exponent is the accurate first step.