To simplify the expression \((3.2 \times 10^{-2})(4.2 \times 10^{6})(5.2 \times 10^{5})\), we can break it down as follows:
-
Multiply the coefficients: \[ 3.2 \times 4.2 \times 5.2 \]
Calculating this step by step:
- \(3.2 \times 4.2 = 13.44\)
- Then, \(13.44 \times 5.2 = 69.728\)
-
Multiply the powers of 10: \[ 10^{-2} \times 10^{6} \times 10^{5} = 10^{-2 + 6 + 5} = 10^{9} \]
-
Combine the results: \[ 69.728 \times 10^{9} \]
This is still not in standard notation, so we need to convert \(69.728\) into a form that has only one digit to the left of the decimal. This means we can express \(69.728\) as \(6.9728 \times 10^{1}\).
- Now we can combine it with \(10^{9}\): \[ 6.9728 \times 10^{1} \times 10^{9} = 6.9728 \times 10^{10} \]
Thus, the simplified expression in standard notation is \(6.9728 \times 10^{10}\).
However, this does not match any of the options provided. If we check the original multiplication for any mistakes:
Calculating the product again:
- Coefficients: \(3.2 \times 4.2 = 13.44\), then \(13.44 \times 5.2 = 69.728\)
- For powers of 10: adding the exponents gives \(10^9\)
Thus, our final combined product of coefficients and exponentials, \(69.728 \times 10^9\) can be expressed in standard notation as \(6.9728 \times 10^{10}\).
There were no mistakes in calculations. Unfortunately, the choices provided do not include this result. Please check if there was a typographical error in the options presented.
1 answer