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)

Question

Responses

none of them
none of them

Charles
Charles

Zayeer
Zayeer

Kali

Answer 1

To simplify \( 1,000^{2/3} \), we need to understand what the expression means.

1. Rewrite \( 1,000 \): \[ 1,000 = 10^3 \]

2. Substitute this into the expression: \[ 1,000^{2/3} = (10^3)^{2/3} \]

3. Use the property of exponents \( (a^m)^n = a^{m \cdot n} \): \[ (10^3)^{2/3} = 10^{3 \cdot (2/3)} = 10^2 \]

4. Calculate \( 10^2 \): \[ 10^2 = 100 \]

Thus, the correct simplification of \( 1,000^{2/3} \) is \( 100 \).

Therefore, Kali is the one who has the correct value.