Charles, Zayeer, and Kali are trying to simplify 1,000 2/3

Question

. 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)

Answer 1

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.