Question
Which expression is equivalent to \( \frac{2^{-3}}{2^{-5}} \) ? (A) \( 2^{2} \) (B) \( \frac{1}{2^{2}} \) (C) \( 2^{8} \) (D) \( \frac{1}{2^{8}} \)
Ask by Ellis Hall. in the United Kingdom
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \( \frac{2^{-3}}{2^{-5}} \) is equivalent to \( 2^{2} \).
Solution
Calculate or simplify the expression \( \frac{2^{-3}}{2^{-5}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{2^{-3}}{2^{-5}}\)
- step1: Multiply by \(a^{-n}:\)
\(2^{-3}\times 2^{5}\)
- step2: Multiply:
\(2^{-3+5}\)
- step3: Add the numbers:
\(2^{2}\)
- step4: Evaluate the power:
\(4\)
The expression \( \frac{2^{-3}}{2^{-5}} \) is equivalent to \( 4 \).
Therefore, the correct answer is (A) \( 2^{2} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{2^{-3}}{2^{-5}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). So, we have: \[ \frac{2^{-3}}{2^{-5}} = 2^{-3 - (-5)} = 2^{-3 + 5} = 2^{2}. \] Thus, the expression is equivalent to \( 2^{2} \), which corresponds to option (A).
