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→1,00023=10⋅10=100 . Who has the correct value?(1 point)

Answer 1

To simplify \( 1,000^{\frac{2}{3}} \), we start by expressing \( 1,000 \) in terms of base \( 10 \):

\[
1,000 = 10^3
\]

Now, substituting this into the expression:

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

Using the exponentiation rule \( (a^m)^n = a^{m \cdot n} \):

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

Now, calculating \( 10^2 \):

\[
10^2 = 100
\]

Thus, the correct simplification of \( 1,000^{\frac{2}{3}} \) is \( 100 \).

Kali is the one who has the correct value.