Question
Calculate. \[ \left(-5.0 \times 10^{12}\right)^{2} \] Write your answer in scientific notation
Ask by Hanson Horton. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \(2.5 \times 10^{25}\).
Solution
Calculate or simplify the expression \( (-5.0 \times 10^{12})^{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(-5\times 10^{12}\right)^{2}\)
- step1: Evaluate the power:
\(2.5\times 10^{25}\)
The result of \((-5.0 \times 10^{12})^{2}\) is \(2.5 \times 10^{25}\) in scientific notation.
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Simplify this solution Extra Insights
To calculate \(\left(-5.0 \times 10^{12}\right)^{2}\), we start by squaring the coefficient and the exponent separately: 1. Squaring the coefficient: \((-5.0)^{2} = 25.0\) 2. Squaring the exponent: \((10^{12})^{2} = 10^{24}\) Now, we combine the results: \[ 25.0 \times 10^{24} \] To express this in proper scientific notation, we convert \(25.0\) into \(2.5\) (which is between 1 and 10) and adjust the exponent accordingly by adding 1 to the exponent of 10: \[ 25.0 \times 10^{24} = 2.5 \times 10^{25} \] Thus, the final answer is: \[ \boxed{2.5 \times 10^{25}} \]
