Question
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Answer
The expression simplifies to 0.8.
Solution
Calculate or simplify the expression \( 5^{-1}/2^{-2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5^{-1}}{2^{-2}}\)
- step1: Rewrite the expression:
\(\frac{\frac{1}{5}}{2^{-2}}\)
- step2: Multiply by the reciprocal:
\(\frac{1}{5}\times 2^{2}\)
- step3: Multiply:
\(\frac{2^{2}}{5}\)
- step4: Evaluate the power:
\(\frac{4}{5}\)
The value of \( \frac{5^{-1}}{2^{-2}} \) is \( \frac{4}{5} \) or 0.8.
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Simplify this solution Extra Insights
To make things easier, remember that \(5^{-1}\) is the same as \(\frac{1}{5}\) and \(2^{-2}\) is \(\frac{1}{2^2} = \frac{1}{4}\). So, you can rewrite the expression as \(\frac{\frac{1}{5}}{\frac{1}{4}}\). Dividing by a fraction is like multiplying by its reciprocal, which gives you \(\frac{1}{5} \times 4 = \frac{4}{5}\)! Now you have the simplified solution, but why stop there? This kind of manipulation is like a cool math magic trick, revealing intricacies of how numbers play together. Remember, every fraction has a story—it’s just waiting for you to unearth it!
