Sure! Let's break down the problem step-by-step to simplify the expression [tex]\(\left(9 \times 10^7\right)\left(7 \times 10^9\right)\)[/tex] and write the answer in scientific notation.
1. Step 1: Write the expression to be simplified.
[tex]\[
(9 \times 10^7) \times (7 \times 10^9)
\][/tex]
2. Step 2: Multiply the coefficients (the numbers in front).
[tex]\[
9 \times 7 = 63
\][/tex]
3. Step 3: Multiply the powers of 10 by adding the exponents.
[tex]\[
10^7 \times 10^9 = 10^{7 + 9} = 10^{16}
\][/tex]
4. Step 4: Combine the results from Steps 2 and 3.
[tex]\[
63 \times 10^{16}
\][/tex]
5. Step 5: Convert this number into proper scientific notation.
To write [tex]\(63 \times 10^{16}\)[/tex] in scientific notation, we need to express the coefficient as a number between 1 and 10. [tex]\(63\)[/tex] can be rewritten as [tex]\(6.3 \times 10^1\)[/tex].
[tex]\[
63 \times 10^{16} = (6.3 \times 10^1) \times 10^{16}
\][/tex]
Using the property of exponents, we can combine the powers of 10:
[tex]\[
(6.3 \times 10^1) \times 10^{16} = 6.3 \times 10^{1 + 16} = 6.3 \times 10^{17}
\][/tex]
6. Step 6: Verify the options.
We compare [tex]\(6.3 \times 10^{17}\)[/tex] with the given multiple choice options:
- [tex]\(6.3 \times 10^{17}\)[/tex]
- [tex]\(1.6 \times 10^{64}\)[/tex]
- [tex]\(1.6 \times 10^{17}\)[/tex]
- [tex]\(6.3 \times 10^{64}\)[/tex]
The correct answer is [tex]\(6.3 \times 10^{17}\)[/tex].
So, the simplified expression in scientific notation is:
[tex]\[
\boxed{6.3 \times 10^{17}}
\][/tex]
