Pregunta
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\( 64^{-\frac{1}{6}} = \frac{1}{2} \)
Solución
To simplify 64^(-1/6), first express 64 as a power of a smaller number. Notice that 64 = 2^6. Substitute this into the expression:
(2^6)^(-1/6)
Now apply the exponent rule (a^b)^c = a^(b*c):
2^(6 * (-1/6)) = 2^(-1)
Since a negative exponent means the reciprocal, 2^(-1) equals:
1/2
Thus, the simplified expression is 1/2.
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Simplifique esta solución The Deep Dive
To simplify \( 64^{-\frac{1}{6}} \), we start by rewriting the expression. The negative exponent indicates that we should take the reciprocal, so \( 64^{-\frac{1}{6}} = \frac{1}{64^{\frac{1}{6}}} \). Next, we know that \( 64 \) can be expressed as \( 2^6 \). Thus, we have: \[ 64^{\frac{1}{6}} = (2^6)^{\frac{1}{6}} = 2^{6 \cdot \frac{1}{6}} = 2^1 = 2. \] Substituting this back into our expression gives: \[ 64^{-\frac{1}{6}} = \frac{1}{64^{\frac{1}{6}}} = \frac{1}{2} = 0.5. \] So, the simplified result of \( 64^{-\frac{1}{6}} \) is \( 0.5 \).
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