To find how many times larger \( 4 \times 10^{10} \) is than \( 2 \times 10^{-4} \), we can divide the two numbers:
\[ \frac{4 \times 10^{10}}{2 \times 10^{-4}} \]
This can be simplified as follows:
\[ = \frac{4}{2} \times \frac{10^{10}}{10^{-4}} \]
Calculating the first part:
\[ \frac{4}{2} = 2 \]
Calculating the second part using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):
\[ \frac{10^{10}}{10^{-4}} = 10^{10 - (-4)} = 10^{10 + 4} = 10^{14} \]
Putting it all together:
\[ 2 \times 10^{14} \]
Thus, \( 4 \times 10^{10} \) is \( 2 \times 10^{14} \) times larger than \( 2 \times 10^{-4} \).
Therefore, the correct response is:
2×10¹⁴ (2 times 10 to the 14th power).