Question
Write each answer as an inte a) \( \left(\frac{2}{3}\right)^{-3} \cdot\left(\frac{2}{3}\right)^{2} \)
Ask by Coles Macdonald. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( \frac{3}{2} \) or \( 1.5 \).
Solution
Calculate or simplify the expression \( (2/3)^{-3}*(2/3)^{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{2}{3}\right)^{-3}\left(\frac{2}{3}\right)^{2}\)
- step1: Multiply:
\(\left(\frac{2}{3}\right)^{-3+2}\)
- step2: Add the numbers:
\(\left(\frac{2}{3}\right)^{-1}\)
- step3: Simplify:
\(\frac{3}{2}\)
The result of \( \left(\frac{2}{3}\right)^{-3} \cdot \left(\frac{2}{3}\right)^{2} \) is \( \frac{3}{2} \) or \( 1\frac{1}{2} \) or \( 1.5 \).
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Simplify this solution Extra Insights
To simplify the expression \( \left(\frac{2}{3}\right)^{-3} \cdot\left(\frac{2}{3}\right)^{2} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \). Applying this, we have: \[ \left(\frac{2}{3}\right)^{-3 + 2} = \left(\frac{2}{3}\right)^{-1} \] Now, to further simplify \( \left(\frac{2}{3}\right)^{-1} \), recall that a negative exponent indicates the reciprocal: \[ \left(\frac{2}{3}\right)^{-1} = \frac{1}{\left(\frac{2}{3}\right)} = \frac{3}{2} \] So the simplified expression is \( \frac{3}{2} \).
