Pregunta
Simplify to a single power of 2 : \[ \frac{2^{8}}{2^{5}} \]
Ask by Marshall Reyes. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified expression is \(2^3\).
Solución
1. Start with the expression:
\[
\frac{2^{8}}{2^{5}}
\]
2. Use the exponent division property:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
3. Apply the property with \(a = 2\), \(m = 8\), and \(n = 5\):
\[
\frac{2^{8}}{2^{5}} = 2^{8-5}
\]
4. Simplify the exponent:
\[
2^{8-5} = 2^3
\]
Thus, the simplified expression is:
\[
2^3
\]
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Simplifique esta solución Bonus Knowledge
To simplify \( \frac{2^{8}}{2^{5}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). So, applying that here: \[ \frac{2^{8}}{2^{5}} = 2^{8-5} = 2^{3} \] Thus, the simplified form is \( 2^{3} \).
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