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

Zayeer
Zayeer

none of them
none of them

Kali

Answer 1

To simplify \( 1000^{2/3} \), we can start by expressing 1000 as \( 10^3 \):

\[
1000 = 10^3
\]

Next, we can apply the exponent:

\[
1000^{2/3} = (10^3)^{2/3}
\]

When we raise a power to another power, we multiply the exponents:

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

Now, simplifying \( 10^2 \) gives us:

\[
10^2 = 100
\]

So the correct simplification of \( 1000^{2/3} \) is indeed 100. Therefore, Kali is the one who has the correct value.

**Final answer: Kali**