Question

Charles, Zayeer. and Kali are trying to simplify 1000 ^ (2/3) Charles says the correct simplification is 10 because 1000 = 10 * 10 * 10 and 1000 ^ (2/3) = 10 Zayeer says the correct simplification is 1,000 because 1000 = 10 * 10 * 10 -> 1000 ^ (2/3) = 10 * 10 * 10 = 1000 Kali says the correct simplification is 100 because 1000 = 10 * 10 * 10 -> 1000 ^ (2/3) = 10 * 10 = 100 Who has the correct value?

Charles
Zayeer
Kali
none of them

Answer 1

To simplify \( 1000^{(2/3)} \), we start by rewriting \( 1000 \).

We know that:

\[
1000 = 10^3
\]

Now substituting this into the expression gives:

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

Using the property of exponents \((a^m)^n = a^{m \cdot n}\):

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

Now we calculate \( 10^2 \):

\[
10^2 = 100
\]

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

Kali is the one who has the correct value.