Question
Half of the number \( 4^{10} \) is \( \begin{array}{lll}\text { (a) } 2^{5} & \text { (b) } 2^{10} & \text { (c) } 2^{19}\end{array} \)
Ask by Barrett Burns. in Egypt
Nov 21,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
نصف \( 4^{10} \) هو \( 2^{19} \). الإجابة الصحيحة هي (c) \( 2^{19} \).
Solution
لحساب نصف العدد \( 4^{10} \)، يمكننا أولاً إعادة كتابة \( 4^{10} \) باستخدام الأساس 2:
\[
4^{10} = (2^2)^{10} = 2^{20}
\]
الآن، نحسب نصف هذا العدد:
\[
\frac{4^{10}}{2} = \frac{2^{20}}{2} = 2^{20 - 1} = 2^{19}
\]
لذا، نصف العدد \( 4^{10} \) هو \( 2^{19} \).
الإجابة الصحيحة هي (c) \( 2^{19} \).
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Simplify this solution Bonus Knowledge
To solve for half of \( 4^{10} \), we can first express \( 4^{10} \) in terms of base 2: \[ 4^{10} = (2^2)^{10} = 2^{20} \] Now, taking half of \( 2^{20} \) gives us: \[ \frac{2^{20}}{2} = 2^{19} \] Thus, half of the number \( 4^{10} \) is \( 2^{19} \). The correct answer is option \( (c) \, 2^{19} \).
