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

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 months ago

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.