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The simplified form is –1/4.
Solución
We start by interpreting the exponent −1/3 as follows:
1. The exponent 1/3 means taking the cube root.
2. The negative sign in the exponent means taking the reciprocal.
So, we have:
(–64)^(−1/3) = 1 / (–64)^(1/3)
Next, compute the cube root of –64:
(–64)^(1/3) = –4, because (–4)^3 = –64.
Finally, taking the reciprocal:
1 / (–4) = –1/4
Thus, the simplified form is –1/4.
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Simplifique esta solución The Deep Dive
To simplify \( (-64)^{-\frac{1}{3}} \), first acknowledge that the negative exponent indicates a reciprocal. Thus, we can rewrite it as \( \frac{1}{(-64)^{\frac{1}{3}}} \). Now, the cube root of \(-64\) is \(-4\) because \((-4) \times (-4) \times (-4) = -64\). Therefore, putting it all together, we get: \[ (-64)^{-\frac{1}{3}} = \frac{1}{-4} = -\frac{1}{4}. \]
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