Question
Charles, Zayeer, and Kali are trying to simplify 1,000 2/3
. Charles says the correct simplification is 10 because 1,000=10⋅10⋅10
and 1,000 2/3=10
. Zayeer says the correct simplification is 1,000 because 1,000=10⋅10⋅10→1,000 2/3=10⋅10⋅10=1,000
. Kali says the correct simplification is 100 because 1,000=10⋅10⋅10→1,000 2/3=10⋅10=100
. Who has the correct value?(1 point)
. Charles says the correct simplification is 10 because 1,000=10⋅10⋅10
and 1,000 2/3=10
. Zayeer says the correct simplification is 1,000 because 1,000=10⋅10⋅10→1,000 2/3=10⋅10⋅10=1,000
. Kali says the correct simplification is 100 because 1,000=10⋅10⋅10→1,000 2/3=10⋅10=100
. Who has the correct value?(1 point)
Answers
Answered by
GPT-4o mini
To determine the correct simplification of \(1,000^{2/3}\), we can break it down as follows:
1. First, express \(1,000\) in terms of powers of \(10\):
\[
1,000 = 10^3.
\]
2. Now, we can substitute \(1,000\) with \(10^3\):
\[
1,000^{2/3} = (10^3)^{2/3}.
\]
3. Use the power of a power property which states that \((a^m)^n = a^{m \cdot n}\):
\[
(10^3)^{2/3} = 10^{3 \cdot (2/3)} = 10^2.
\]
4. Calculate \(10^2\):
\[
10^2 = 100.
\]
Therefore, the correct simplification is \(100\).
Kali is the one who has the correct value.
1. First, express \(1,000\) in terms of powers of \(10\):
\[
1,000 = 10^3.
\]
2. Now, we can substitute \(1,000\) with \(10^3\):
\[
1,000^{2/3} = (10^3)^{2/3}.
\]
3. Use the power of a power property which states that \((a^m)^n = a^{m \cdot n}\):
\[
(10^3)^{2/3} = 10^{3 \cdot (2/3)} = 10^2.
\]
4. Calculate \(10^2\):
\[
10^2 = 100.
\]
Therefore, the correct simplification is \(100\).
Kali is the one who has the correct value.