multiplication and division with powers of ten\n$8 \\cdot 10^4$ is how many times as large as $4 \\cdot…

multiplication and division with powers of ten\n$8 \\cdot 10^4$ is how many times as large as $4 \\cdot 10^{-5}$?\nchoose 1 answer:\na $2 \\cdot 10^{-9}$\nb $4 \\cdot 10^{-1}$\nc $4 \\cdot 10^1$\nd $2 \\cdot 10^9$

multiplication and division with powers of ten\n$8 \\cdot 10^4$ is how many times as large as $4 \\cdot 10^{-5}$?\nchoose 1 answer:\na $2 \\cdot 10^{-9}$\nb $4 \\cdot 10^{-1}$\nc $4 \\cdot 10^1$\nd $2 \\cdot 10^9$

Answer

Explanation:

Step1: Set up the division

To find how many times (8 \cdot 10^{4}) is as large as (4 \cdot 10^{-5}), we divide (8 \cdot 10^{4}) by (4 \cdot 10^{-5}). So the expression is (\frac{8 \cdot 10^{4}}{4 \cdot 10^{-5}}).

Step2: Divide the coefficients and the powers of ten separately

First, divide the coefficients: (\frac{8}{4} = 2). Then, divide the powers of ten using the rule ( \frac{10^{a}}{10^{b}} = 10^{a - b}). So (\frac{10^{4}}{10^{-5}} = 10^{4 - (-5)} = 10^{4 + 5} = 10^{9}).

Step3: Multiply the results

Multiply the coefficient result and the power of ten result: (2 \cdot 10^{9}).

Answer:

D. (2 \cdot 10^{9})