Question

Charles, Zayeer, and Kali are trying to simplify 1,00023
. 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→1,00023=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

Kali
Kali

Charles
Charles

none of them
none of them

Zayeer

Answer 1

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

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

Using the power of a power property of exponents, we multiply the exponents:

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

Calculating \( 10^2 \):

\[
10^2 = 100
\]

So, the correct simplification of \( 1000^{2/3} \) is \( 100 \).

Thus, Kali has the correct value.