Pregunta
Which expression is equivalent to \( \frac{2^{3}}{2^{7}} \) ? - \( \frac{1}{2^{4}} 2^{4} \)-2
Ask by Valdez Lynch. in the United States
Mar 17,2025
Solución de inteligencia artificial de Upstudy
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The expression equivalent to \( \frac{2^{3}}{2^{7}} \) is \( \frac{1}{2^{4}} \).
Solución
We start with the expression
\[
\frac{2^3}{2^7}.
\]
Using the law of exponents for division, we subtract the exponents:
\[
\frac{2^3}{2^7} = 2^{3-7} = 2^{-4}.
\]
A negative exponent indicates the reciprocal:
\[
2^{-4} = \frac{1}{2^4}.
\]
Thus, the expression equivalent to \(\frac{2^3}{2^7}\) is
\[
\frac{1}{2^4}.
\]
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Simplifique esta solución Extra Insights
Let’s simplify \( \frac{2^{3}}{2^{7}} \). According to the laws of exponents, when you divide like bases, you subtract the exponents. So, \( \frac{2^{3}}{2^{7}} = 2^{3-7} = 2^{-4} \). This can also be rewritten as \( \frac{1}{2^{4}} \). Now, if we check the provided option, \( \frac{1}{2^{4}} \) suggests we’re lucky to have an equivalent expression lurking there! It's like finding a gem hidden in the sand: understanding the laws of exponents simplifies problems and reveals treasures like equivalent expressions in no time! So, our answer is indeed \( \frac{1}{2^{4}} \).
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