Question

How many times larger is 4×10^10
than 2×10^−4?
(1 point)
Responses

2×106
2 times 10 to the 6th power

2×1040
2 times 10 to the 40th power

2×1014
2 times 10 to the 14th power

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

Answer 1

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

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

We can separate the constants and the powers of ten:

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

Calculating the constant:

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

Now, for the powers of ten, we subtract the exponents:

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

Now putting it all together:

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

Thus, \( 4 \times 10^{10} \) 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)