Charles, Zayeer, and Kali are trying to simplify 1,00023

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

Zayeer
Zayeer

Kali
Kali

Charles
Charles

none of them

Answer 1

To simplify \( 1,000^{2/3} \), we start by rewriting \( 1,000 \) in terms of powers of \( 10 \):

\[ 1,000 = 10^3 \]

Now, we can substitute this into the expression:

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

Using the rules of exponents, we can multiply the exponents:

\[ (10^3)^{2/3} = 10^{3 \cdot \frac{2}{3}} = 10^{2} = 100 \]

So, the correct simplification is 100.

Thus, Kali is the one who has the correct value. The answer is:

Kali