1.

Question

Charles, Zayeer, and Kali are trying to simplify 1000 2/3
.

Charles says the correct simplification is 10 because 1000=10⋅10⋅10
and 1000 2/3=10
100023=10
.

Zayeer says that the correct simplification is 1000 because 1000=10⋅10⋅10→1000 2/3=10⋅10⋅10=1000
.

Kali says the correct simplification is 100 because 1000=10⋅10⋅10→1000 2/3=10⋅10=100

Answer 1

To simplify \(1000^{2/3}\), we can use the property of exponents.

The expression \(1000^{2/3}\) can be interpreted as follows:

1. First, rewrite \(1000\) as \(10^3\). Thus, we have:

\[ 1000^{2/3} = (10^3)^{2/3} \]

2. When raising a power to another power, we multiply the exponents:

\[ (10^3)^{2/3} = 10^{3 \cdot \frac{2}{3}} = 10^2 \]

3. Finally, simplify \(10^2\):

\[ 10^2 = 100 \]

Therefore, the correct simplification of \(1000^{2/3}\) is \(100\).

So, Kali is correct in this case, while Charles is incorrect because he mistakenly simplified it to \(10\), and Zayeer is also incorrect because he claimed it remains \(1000\). The correct answer is indeed \(100\).