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→1,0002/3=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
Zayeer
Zayeer
none of them
none of them
Kali

Answer 1

To simplify \( 1,000^{2/3} \), we start by expressing \( 1,000 \) in terms of its prime factors:

\[
1,000 = 10^3
\]

Now we can rewrite \( 1,000^{2/3} \):

\[
1,000^{2/3} = (10^3)^{2/3}
\]

Using the exponent multiplication rule \( (a^m)^n = a^{m \cdot n} \), we get:

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

Calculating \( 10^2 \):

\[
10^2 = 100
\]

Thus, \( 1,000^{2/3} = 100 \).

Kali is the one who correctly identifies the simplification. Therefore, the correct answer is:

**Kali**.