What is the numerical value of the expression (2/3)^(-2)?
Answer and explanation
Correct answer: C. 9/4 (or 2.25)
- Step 1: A negative exponent indicates the reciprocal: (a/b)^(-n) = (b/a)^n. Step 2. (2/3)^(-2) = (3/2)^2 = 3^2 / 2^2 = 9/4 = 2.25. Answer: 9/4 (or 2.25), inverting the fraction to (3/2)^2 and squaring both terms. Why not the others: 4/9 ignores the negative sign in the exponent; negative powers do not produce negative numbers from positive bases.
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