Question
Simplify the following. Use the \( { }^{\wedge} \) symbol for the exponent if needed. \( \left(\frac{2}{3}\right)^{-1} \)
Ask by Rodriquez Brooks. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\frac{3}{2}\)
Solution
To simplify \( \left(\frac{2}{3}\right)^{-1} \), you can use the property of exponents that states:
\[
\left(\frac{a}{b}\right)^{-1} = \frac{b}{a}
\]
Applying this property:
\[
\left(\frac{2}{3}\right)^{-1} = \frac{3}{2}
\]
**Simplified form:**
\[
\frac{3}{2}
\]
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Simplify this solution The Deep Dive
To simplify \( \left(\frac{2}{3}\right)^{-1} \), we apply the rule that states raising a fraction to a negative exponent means taking the reciprocal of that fraction and making the exponent positive. This gives us: \[ \left(\frac{2}{3}\right)^{-1} = \frac{1}{\left(\frac{2}{3}\right)} = \frac{3}{2}. \] Thus, the simplified form is \( \frac{3}{2} \).
