Question
Calculate. \[ \left(5.00 \times 10^{7}\right)^{3} \] Write your answer in scientific notation.
Ask by Bowers Adkins. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(1.25 \times 10^{23}\)
Solution
Calculate or simplify the expression \( (5.00 \times 10^{7})^{3} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(5\times 10^{7}\right)^{3}\)
- step1: Evaluate the power:
\(1.25\times 10^{23}\)
The result of \((5.00 \times 10^{7})^{3}\) is \(1.25 \times 10^{23}\) in scientific notation.
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Simplify this solution Extra Insights
To calculate \(\left(5.00 \times 10^{7}\right)^{3}\), you can utilize the properties of exponents. First, raise the coefficient to the power of 3: \[ (5.00)^{3} = 125.000 \] Next, apply the exponent to the power of ten: \[ (10^{7})^{3} = 10^{21} \] Now, combine these results: \[ 125.000 \times 10^{21} \] To express this in proper scientific notation, you need to represent it as \(1.25 \times 10^{23}\) by moving the decimal point in the coefficient one place to the left and increasing the exponent by 1. Thus, the answer in scientific notation is: \[ \boxed{1.25 \times 10^{23}} \]
