Question
Calculate. \[ \left(2 \times 10^{2}\right)\left(2 \times 10^{4}\right) \] Write your answer in scientific nota
Ask by Howell Schwartz. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \(4 \times 10^{6}\).
Solution
To calculate the expression:
\[
\left(2 \times 10^{2}\right)\left(2 \times 10^{4}\right)
\]
**Step 1:** Multiply the coefficients (the numbers in front):
\[
2 \times 2 = 4
\]
**Step 2:** Multiply the powers of 10 by adding their exponents:
\[
10^{2} \times 10^{4} = 10^{2+4} = 10^{6}
\]
**Step 3:** Combine the results from Step 1 and Step 2:
\[
4 \times 10^{6}
\]
**Final Answer:**
\[
4 \times 10^{6}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the expression \((2 \times 10^{2})(2 \times 10^{4})\), we can break it down: First, multiply the coefficients: \(2 \times 2 = 4\). Next, when multiplying the powers of ten, you add the exponents: \(10^{2} \times 10^{4} = 10^{(2+4)} = 10^{6}\). Putting it all together, we have: \[ 4 \times 10^{6} \] So the answer in scientific notation is: \[ 4 \times 10^{6} \]
