Which shows the expression below in simplified form?

(5.6 × 10^8) ÷ (8 × 10^5)
A.
7 × 10^1
B.
-2.4 × 10^2
C.
7 × 10^4
D.
7 × 10^2

1 answer

To simplify the expression \((5.6 × 10^8) ÷ (8 × 10^5)\), we can separate the numerical coefficients and the powers of ten:

  1. Divide the coefficients: \[ \frac{5.6}{8} = 0.7 \]

  2. Divide the powers of ten: \[ \frac{10^8}{10^5} = 10^{8-5} = 10^3 \]

  3. Combine the results: \[ 0.7 × 10^3 \]

  4. Convert \(0.7\) to scientific notation: \[ 0.7 = 7 × 10^{-1} \] Therefore, \[ 0.7 × 10^3 = 7 × 10^{-1} × 10^3 = 7 × 10^{3-1} = 7 × 10^2 \]

Now we can compare the result \(7 × 10^2\) with the given options.

The correct answer is: D. \(7 × 10^2\).