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-----1,000^2/3 = 10*10 = 100. Who has the correct value

Question

zayeer
none of them
kali
charles

Answer 1

Let's analyze the expression \( 1000^{2/3} \) step by step.

First, we can express 1000 in terms of its prime factorization: \[ 1000 = 10^3 \]

Now, substituting this into the original expression: \[ 1000^{2/3} = (10^3)^{2/3} \]

When you raise a power to a power, you multiply the exponents: \[ (10^3)^{2/3} = 10^{(3 \cdot \frac{2}{3})} = 10^2 \]

Now, solving \( 10^2 \): \[ 10^2 = 100 \]

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

Therefore, Kali has the correct value.