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\( 16^{-\frac{3}{4}} = \frac{1}{8} \)
Solución
To simplify 16^(–3/4), follow these steps:
1. Recognize that 16 can be written as 2^4.
2. Substitute this into the expression: (2^4)^(–3/4).
3. Use the power rule: (a^m)^n = a^(m*n). Here, 4*(–3/4) = –3.
4. So, (2^4)^(–3/4) = 2^(–3) = 1/(2^3) = 1/8.
Thus, the simplified form is 1/8.
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Simplifique esta solución The Deep Dive
To simplify \( 16^{-\frac{3}{4}} \), we can first rewrite \( 16 \) as \( 2^4 \). Therefore, \( 16^{-\frac{3}{4}} \) becomes \( (2^4)^{-\frac{3}{4}} \). By using the power of a power rule, we can multiply the exponents: \[ (2^4)^{-\frac{3}{4}} = 2^{4 \cdot -\frac{3}{4}} = 2^{-3}. \] Now, we can simplify \( 2^{-3} \) to \( \frac{1}{2^3} = \frac{1}{8} \). So, \( 16^{-\frac{3}{4}} = \frac{1}{8} \).
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