Question
Calculate \[ \left(5 \times 10^{8}\right)^{-2} \] Write your answer in scientific notation.
Ask by Mccarthy Carrillo. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(4 \times 10^{-18}\)
Solution
Calculate or simplify the expression \( (5 \times 10^{8})^{-2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(5\times 10^{8}\right)^{-2}\)
- step1: Express with a positive exponent:
\(\frac{1}{\left(5\times 10^{8}\right)^{2}}\)
- step2: Evaluate the power:
\(\frac{1}{2.5\times 10^{17}}\)
- step3: Separate the fraction:
\(\frac{1}{2.5}\times \frac{1}{10^{17}}\)
- step4: Divide:
\(0.4\times \frac{1}{10^{17}}\)
- step5: Divide:
\(0.4\times 10^{-17}\)
- step6: Rewrite the number:
\(4\times 10^{-18}\)
The result of \((5 \times 10^{8})^{-2}\) is \(4 \times 10^{-18}\) in scientific notation.
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Simplify this solution Beyond the Answer
To calculate \( \left(5 \times 10^{8}\right)^{-2} \), we can break it down into two parts: the coefficient and the power of ten. First, we take the coefficient: \[ (5)^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04 \] Next, we handle the exponent on the power of ten: \[ (10^{8})^{-2} = 10^{-16} \] Now we combine these two results: \[ 0.04 \times 10^{-16} \] To express \(0.04\) in scientific notation: \[ 0.04 = 4.0 \times 10^{-2} \] Thus, we can rewrite our expression: \[ 4.0 \times 10^{-2} \times 10^{-16} = 4.0 \times 10^{-2 - 16} = 4.0 \times 10^{-18} \] Therefore, the final answer is: \[ \boxed{4.0 \times 10^{-18}} \]
