Charles, Zayeer, and Kali are trying to simplify 1,000^2/3

Question

. 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

Kali

Charles

none of them

Zayeer

Answer 1

To simplify \( 1,000^{2/3} \), let's start by rewriting \( 1,000 \) in base 10:

\[ 1,000 = 10^3 \]

Now, substituting this into the expression:

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

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

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

Calculating the exponent:

\[ 3 \cdot \frac{2}{3} = 2 \]

Thus, we have:

\[ 10^{2} = 100 \]

So the correct value is \( 100 \).

Therefore, Kali is correct.