Question
Work out \( \left(3 \times 10^{4}\right) \times\left(2 \times 10^{9}\right) \) Give your answer in standard index form.
Ask by Sullivan Ryan. in the United Kingdom
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 6 \times 10^{13} \)
Solution
Calculate or simplify the expression \( (3*10^4)*(2*10^9) \).
Calculate the value by following steps:
- step0: Calculate:
\(3\times 10^{4}\times 2\times 10^{9}\)
- step1: Multiply the numbers:
\(6\times 10^{4}\times 10^{9}\)
- step2: Multiply:
\(6\times 10^{13}\)
The result of \( \left(3 \times 10^{4}\right) \times\left(2 \times 10^{9}\right) \) in standard index form is \( 6 \times 10^{13} \).
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Simplify this solution Bonus Knowledge
To solve \( \left(3 \times 10^{4}\right) \times\left(2 \times 10^{9}\right) \), you can multiply the coefficients (the numbers before the powers of ten) and then add the exponents. 1. Multiply the coefficients: \( 3 \times 2 = 6 \). 2. Add the exponents: \( 10^{4} \times 10^{9} = 10^{(4 + 9)} = 10^{13} \). Putting it all together, you get \( 6 \times 10^{13} \). So, the answer in standard index form is \( 6 \times 10^{13} \).
