How many times larger is 4×1010

Question

than 2×10−4
?

(1 point)
Responses

2×106
2 times 10 to the 6th power

2×1014
2 times 10 to the 14th power

2×10−40
2 times 10 to the negative 40 power

2×1040

Answer 1

To find out how many times larger \( 4 \times 10^{10} \) is than \( 2 \times 10^{-4} \), you can divide the two numbers:

\[ \frac{4 \times 10^{10}}{2 \times 10^{-4}} \]

First, divide the coefficients:

\[ \frac{4}{2} = 2 \]

Next, divide the powers of ten by subtracting the exponents:

\[ 10^{10 - (-4)} = 10^{10 + 4} = 10^{14} \]

Now combine the results:

\[ 2 \times 10^{14} \]

So, \( 4 \times 10^{10} \) is \( 2 \times 10^{14} \) times larger than \( 2 \times 10^{-4} \).

The correct response is:

2×10^14 2 times 10 to the 14th power