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

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Get ready for the ALEKS Basic Math Placement Test. Study with interactive quizzes and detailed explanations. Prepare to excel!

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In the expression (7/2)^-2, what mathematical operation does the negative exponent indicate?

Addition
Subtraction
Reciprocal
Square

The correct answer is: Reciprocal

In the expression $ (7/2)^{-2} $, the negative exponent indicates that we need to take the reciprocal of the base raised to the absolute value of the exponent. The base in this case is $ 7/2 $ and the exponent is -2. To simplify, we first find the reciprocal of $ 7/2 $, which is $ 2/7 $. Then we raise this reciprocal to the positive exponent 2. Therefore, $ (7/2)^{-2} $ can be rewritten as $ (2/7)^2 $. When we calculate $ (2/7)^2 $, we multiply $ 2 $ by itself and $ 7 $ by itself, which results in $ 4/49 $. This process clearly demonstrates that the negative exponent signifies taking the reciprocal of the base raised to the power of the absolute value of the negative exponent. Hence, the correct answer is the reciprocal operation.