Alright, let's simplify the expression step-by-step:
We have the expression:
[tex]\[ 6 \cdot \left(9 \times 10^7\right) \cdot \left(7 \times 10^9\right) \][/tex]
#### Step 1: Simplify the expression by combining the constants.
First, we need to combine the numerical constants.
[tex]\[ 6 \cdot 9 \cdot 7 = 378 \][/tex]
#### Step 2: Simplify the powers of 10.
Next, we handle the powers of ten.
[tex]\[ 10^7 \times 10^9 = 10^{7 + 9} = 10^{16} \][/tex]
#### Step 3: Combine the results from Step 1 and Step 2.
Combining the results of the constants and the powers of ten, we get:
[tex]\[ 378 \times 10^{16} \][/tex]
#### Step 4: Convert the coefficient to scientific notation.
To write the result in proper scientific notation, we adjust the coefficient 378 to be a number between 1 and 10. This adjustment involves rewriting 378 as:
[tex]\[ 3.78 \times 10^2 \][/tex]
Thus, we can combine it with the original power of ten:
[tex]\[ 3.78 \times 10^2 \times 10^{16} = 3.78 \times 10^{2+16} = 3.78 \times 10^{18} \][/tex]
#### Final result:
The simplified expression in scientific notation is:
[tex]\[ 3.78 \times 10^{18} \][/tex]
Given the choices:
- [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]
None of these match. So based on your own detailed solution, the correct simplification is [tex]\( 3.78 \times 10^{18} \)[/tex].
The result does not match any of the given options, but the accurate and simplified scientific notation for the expression [tex]\( 6 \cdot \left(9 \times 10^7\right) \cdot \left(7 \times 10^9\right) \)[/tex] is indeed [tex]\( 3.78 \times 10^{18} \)[/tex].
