Question
How many times less is 10 to the power of 2 than 10 to the power of 6 ? Express your answer as an integer power of 10.(1 point)
Responses
10 to the power of −4
10 superscript negative 4 baseline
10,000
10,000
10 to the power of 4
10 superscript 4 baseline
0.0001
0.0001
Responses
10 to the power of −4
10 superscript negative 4 baseline
10,000
10,000
10 to the power of 4
10 superscript 4 baseline
0.0001
0.0001
Answers
GPT-4o mini
To determine how many times less \( 10^2 \) is than \( 10^6 \), you can set up the problem as follows:
\[
\frac{10^2}{10^6}
\]
Using the properties of exponents, this simplifies to:
\[
10^{2 - 6} = 10^{-4}
\]
Thus, \( 10^2 \) is \( 10^{-4} \) times less than \( 10^6 \).
The correct answer is:
\[
10 \text{ to the power of } -4
\]
\[
\frac{10^2}{10^6}
\]
Using the properties of exponents, this simplifies to:
\[
10^{2 - 6} = 10^{-4}
\]
Thus, \( 10^2 \) is \( 10^{-4} \) times less than \( 10^6 \).
The correct answer is:
\[
10 \text{ to the power of } -4
\]