Pregunta
Calculate \[ \left(-2.00 \times 10^{6}\right)^{-3} \] Write your answer in scientific notation.
Ask by Flynn Davey. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
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The answer is \(-1.25 \times 10^{-19}\).
Solución
Calculate or simplify the expression \( (-2.00 \times 10^{6})^{-3} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(-2\times 10^{6}\right)^{-3}\)
- step1: Express with a positive exponent:
\(\frac{1}{\left(-2\times 10^{6}\right)^{3}}\)
- step2: Evaluate the power:
\(\frac{1}{-8\times 10^{18}}\)
- step3: Separate the fraction:
\(\frac{1}{-8}\times \frac{1}{10^{18}}\)
- step4: Divide:
\(-0.125\times \frac{1}{10^{18}}\)
- step5: Divide:
\(-0.125\times 10^{-18}\)
- step6: Rewrite the number:
\(-1.25\times 10^{-19}\)
The result of \((-2.00 \times 10^{6})^{-3}\) is \(-1.25 \times 10^{-19}\) in scientific notation.
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Simplifique esta solución Beyond the Answer
To calculate \((-2.00 \times 10^{6})^{-3}\), we can break it down into two parts: the coefficient and the power of ten. 1. **Calculate the coefficient**: \[ (-2.00)^{-3} = -\frac{1}{(2.00)^3} = -\frac{1}{8.00} = -0.125 \] 2. **Calculate the power of ten**: \[ (10^{6})^{-3} = 10^{-18} \] Now, combine both parts: \[ -0.125 \times 10^{-18} \] To convert \(-0.125\) into scientific notation, we can represent it as: \[ -1.25 \times 10^{-1} \] So we have: \[ -1.25 \times 10^{-1} \times 10^{-18} = -1.25 \times 10^{-19} \] Therefore, the final answer in scientific notation is: \[ \boxed{-1.25 \times 10^{-19}} \]
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