To solve the given multiplication and express the result in proper scientific notation, let's follow these steps:
1. Rewrite the expression using the properties of exponents:
The given expression is:
[tex]\[
\left(6.0 \times 10^5\right) \times \left(4.0 \times 10^6\right)
\][/tex]
When multiplying numbers in scientific notation, you can multiply the coefficients (the numbers before the exponents) and add the exponents.
2. Multiply the coefficients:
[tex]\[
6.0 \times 4.0 = 24.0
\][/tex]
3. Add the exponents:
[tex]\[
10^5 \times 10^6 = 10^{5+6} = 10^{11}
\][/tex]
Therefore, the expression now looks like:
[tex]\[
24.0 \times 10^{11}
\][/tex]
4. Express in scientific notation:
Scientific notation requires the coefficient to be a number between 1 and 10. Here, our coefficient is 24.0, which is not between 1 and 10. To adjust it, we can rewrite 24.0 as 2.4 multiplied by 10:
[tex]\[
24.0 = 2.4 \times 10^1
\][/tex]
5. Combine coefficients and exponents:
[tex]\[
24.0 \times 10^{11} = (2.4 \times 10^1) \times 10^{11}
\][/tex]
Adding the exponents together:
[tex]\[
2.4 \times 10^{1+11} = 2.4 \times 10^{12}
\][/tex]
So, the correct scientific notation for the product is:
[tex]\[
2.4 \times 10^{12}
\][/tex]
Therefore, the correct answer is:
[tex]\[
2.4 \times 10^{12}
\][/tex]
