Answer :
To simplify the expression \(\left(5 \times 10^7\right)\left(6 \times 10^4\right)\) and write the answer using scientific notation, follow these steps:
1. Multiply the coefficients:
[tex]\[ 5 \times 6 = 30 \][/tex]
2. Add the exponents (since the bases are the same and we're multiplying):
[tex]\[ 10^7 \times 10^4 = 10^{7+4} = 10^{11} \][/tex]
3. Combine the results from the steps above:
[tex]\[ 30 \times 10^{11} \][/tex]
4. Convert to scientific notation: In scientific notation, a number is written as \(a \times 10^b\) where \(1 \leq a < 10\). Here, 30 can be written as \(3.0 \times 10^1\) to maintain the format:
[tex]\[ 30 \times 10^{11} = 3.0 \times 10^1 \times 10^{11} = 3.0 \times 10^{1+11} = 3.0 \times 10^{12} \][/tex]
Therefore, the expression \(\left(5 \times 10^7\right)\left(6 \times 10^4\right)\) simplifies to \(3.0 \times 10^{12}\).
So, the correct answer is:
[tex]\[ 3.0 \times 10^{12} \][/tex]
1. Multiply the coefficients:
[tex]\[ 5 \times 6 = 30 \][/tex]
2. Add the exponents (since the bases are the same and we're multiplying):
[tex]\[ 10^7 \times 10^4 = 10^{7+4} = 10^{11} \][/tex]
3. Combine the results from the steps above:
[tex]\[ 30 \times 10^{11} \][/tex]
4. Convert to scientific notation: In scientific notation, a number is written as \(a \times 10^b\) where \(1 \leq a < 10\). Here, 30 can be written as \(3.0 \times 10^1\) to maintain the format:
[tex]\[ 30 \times 10^{11} = 3.0 \times 10^1 \times 10^{11} = 3.0 \times 10^{1+11} = 3.0 \times 10^{12} \][/tex]
Therefore, the expression \(\left(5 \times 10^7\right)\left(6 \times 10^4\right)\) simplifies to \(3.0 \times 10^{12}\).
So, the correct answer is:
[tex]\[ 3.0 \times 10^{12} \][/tex]
