use the exponent function on your calculator (ee or exp) to compute the following.

(-1.6 x 10^5) (-2.4 x 10^15)
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8.9 x 10^3

1 answer

To compute the expression

\[ \frac{(-1.6 \times 10^5) \times (-2.4 \times 10^{15})}{8.9 \times 10^3} \]

we can break it down into a few steps:

  1. Multiply the numerators: \[ (-1.6) \times (-2.4) = 3.84 \] \[ 10^5 \times 10^{15} = 10^{(5 + 15)} = 10^{20} \] Therefore, \[ (-1.6 \times 10^5) \times (-2.4 \times 10^{15}) = 3.84 \times 10^{20} \]

  2. Now divide by the denominator: \[ \frac{3.84 \times 10^{20}}{8.9 \times 10^3} \]

    First, divide the coefficients: \[ \frac{3.84}{8.9} \approx 0.43146 \]

    Now, handle the powers of ten: \[ \frac{10^{20}}{10^3} = 10^{(20 - 3)} = 10^{17} \]

  3. Combine the results: \[ 0.43146 \times 10^{17} \]

  4. Expressing in scientific notation: To convert \(0.43146\) to scientific notation, we write it as: \[ 4.3146 \times 10^{-1} \] Combining this with \(10^{17}\): \[ 4.3146 \times 10^{-1} \times 10^{17} = 4.3146 \times 10^{16} \]

Thus, the final result is: \[ 4.3146 \times 10^{16} \]