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\( (256)^{\frac{3}{4}} = 64 \)
Solución
To evaluate (256)^(3/4), we can follow these steps:
1. Recognize that the exponent 3/4 indicates the fourth root of 256 raised to the power of 3:
(256)^(3/4) = [(256)^(1/4)]^3
2. Find the fourth root of 256. Since 4⁴ = 256, we have:
(256)^(1/4) = 4
3. Now, raise 4 to the power of 3:
4³ = 64
Thus, (256)^(3/4) = 64.
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Simplifique esta solución Bonus Knowledge
To evaluate \( (256)^{\frac{3}{4}} \), we start by rewriting \( 256 \) as a power of \( 2 \). Since \( 256 = 2^8 \), we can substitute this into our expression: \[ (256)^{\frac{3}{4}} = (2^8)^{\frac{3}{4}} \] Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify this further: \[ (2^8)^{\frac{3}{4}} = 2^{8 \cdot \frac{3}{4}} = 2^{6} \] Now we can evaluate \( 2^6 \): \[ 2^6 = 64 \] Thus, the value of \( (256)^{\frac{3}{4}} \) is \( \boxed{64} \).
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