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

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)
Responses

Charles
    Charles
    none of them
    none of them
    Kali
    Kali
    Zayeer

GPT-4o mini · Answer

To simplify $ 1000^{2/3} $, we start by rewriting 1000 in terms of powers of 10: $$ 1000 = 10^3 $$ Now, substituting this into the expression: $$ 1000^{2/3} = (10^3)^{2/3} $$ Using the properties of exponents, we can simplify this further: $$ (10^3)^{2/3} = 10^{3 \cdot (2/3)} = 10^2 = 100 $$ Therefore, the correct simplification of $ 1000^{2/3} $ is $ 100 $. Thus, Kali has the correct value.