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

1 answer

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.