Question
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Answer
\(3.5^{-2} \approx 0.081633\) or \(\frac{4}{49}\).
Solution
Calculate or simplify the expression \( 3.5^{-2} \).
Calculate the value by following steps:
- step0: Calculate:
\(3.5^{-2}\)
- step1: Convert the expressions:
\(\left(\frac{7}{2}\right)^{-2}\)
- step2: Transform the expression:
\(\left(\frac{2}{7}\right)^{2}\)
- step3: Use the properties of exponents:
\(\frac{2^{2}}{7^{2}}\)
- step4: Evaluate the power:
\(\frac{4}{7^{2}}\)
- step5: Evaluate the power:
\(\frac{4}{49}\)
The value of \(3.5^{-2}\) is approximately 0.081633 or \(\frac{4}{49}\).
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Simplify this solution Extra Insights
To evaluate \( 3.5^{-2} \), remember that a negative exponent signifies the reciprocal of the base raised to the positive exponent. Hence, \( 3.5^{-2} \) is the same as \( \frac{1}{3.5^2} \). Now you just need to calculate \( 3.5^2 \), which equals 12.25. So, \( 3.5^{-2} = \frac{1}{12.25} \approx 0.0816 \). When working with negative exponents, a common mistake is to forget to take the reciprocal altogether. Always double-check that you’re flipping the base when you encounter a negative exponent. It’s a small detail that can trip up even the most seasoned math enthusiasts!
