Question
How many times larger is 4×1010
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
Answers
GPT-4o mini
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)**.
\[
\frac{4 \times 10^{10}}{2 \times 10^{-4}}
\]
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)**.