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.