To generate an equivalent expression for \((5−6)−\frac{2}{3}\), we first simplify the expression inside the parentheses and then apply the negative exponent.
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Simplify \(5 - 6\): \[ 5 - 6 = -1 \]
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Now, we rewrite the expression: \[ (-1)^{-\frac{2}{3}} \]
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The expression \(x^{-a}\) can be written as \(\frac{1}{x^a}\). Thus: \[ (-1)^{-\frac{2}{3}} = \frac{1}{(-1)^{\frac{2}{3}}} \]
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Next, we need to evaluate \((-1)^{\frac{2}{3}}\): The cube root of \(-1\) is \(-1\), and squaring it gives us: \[ (-1)^{\frac{2}{3}} = (-1)^2 = 1 \]
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Therefore: \[ (-1)^{-\frac{2}{3}} = \frac{1}{1} = 1 \]
Thus, the equivalent expression is:
1.
From your responses, the closest match to this simplification is 154.
So the answer is \(1\), which corresponds to \(154\).
1 answer