Answer :
To simplify the given expression [tex]\(\left(9.78 \times 10^{-11}\right)\left(3.4 \times 10^{-18}\right)\)[/tex] and write the final answer in scientific notation, we can follow these steps:
1. Multiply the coefficients:
[tex]\[ 9.78 \times 3.4 = 33.252 \][/tex]
2. Add the exponents:
[tex]\[ -11 + (-18) = -11 - 18 = -29 \][/tex]
3. Combine the results:
[tex]\[ 33.252 \times 10^{-29} \][/tex]
However, this form is not yet in standard scientific notation. In scientific notation, the coefficient should be a number between 1 and 10. So, we need to adjust it:
4. Adjust the coefficient:
[tex]\[ 33.252 = 3.3252 \times 10^1 \][/tex]
5. Adjust the exponent accordingly:
[tex]\[ 33.252 \times 10^{-29} = (3.3252 \times 10^1) \times 10^{-29} = 3.3252 \times 10^{1 + (-29)} = 3.3252 \times 10^{-28} \][/tex]
Thus, the final answer in scientific notation is:
[tex]\[ 3.3252 \times 10^{-28} \][/tex]
Hence, the correct option is:
[tex]\[ \boxed{3.3252 \times 10^{-28}} \][/tex]
1. Multiply the coefficients:
[tex]\[ 9.78 \times 3.4 = 33.252 \][/tex]
2. Add the exponents:
[tex]\[ -11 + (-18) = -11 - 18 = -29 \][/tex]
3. Combine the results:
[tex]\[ 33.252 \times 10^{-29} \][/tex]
However, this form is not yet in standard scientific notation. In scientific notation, the coefficient should be a number between 1 and 10. So, we need to adjust it:
4. Adjust the coefficient:
[tex]\[ 33.252 = 3.3252 \times 10^1 \][/tex]
5. Adjust the exponent accordingly:
[tex]\[ 33.252 \times 10^{-29} = (3.3252 \times 10^1) \times 10^{-29} = 3.3252 \times 10^{1 + (-29)} = 3.3252 \times 10^{-28} \][/tex]
Thus, the final answer in scientific notation is:
[tex]\[ 3.3252 \times 10^{-28} \][/tex]
Hence, the correct option is:
[tex]\[ \boxed{3.3252 \times 10^{-28}} \][/tex]
