Question
Rewrite the following without an exponent. \[ \left(\frac{2}{3}\right)^{-1} \]
Ask by Rodriguez Reeves. in the United States
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{3}{2}\)
Solution
To remove the exponent, recall that any nonzero number raised to the power of –1 is its reciprocal. Thus,
(2/3)^(–1) = 1 / (2/3) = 3/2.
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Simplify this solution Beyond the Answer
To rewrite \(\left(\frac{2}{3}\right)^{-1}\) without an exponent, we can use the property of negative exponents. Specifically, a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. Therefore, \[ \left(\frac{2}{3}\right)^{-1} = \frac{1}{\frac{2}{3}}. \] When we take the reciprocal, this simplifies to \[ \frac{3}{2}. \] So, the final answer is \(\frac{3}{2}\).
