Question

Charles, Zayeer, and Kali are trying to simplify 1,00023 . Charles says the correct simplification is 10 because 1,000=10⋅10⋅10 and 1,00023=10 . Zayeer says the correct simplification is 1,000 because 1,000=10⋅10⋅10→1,00023=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?

Answer 1

To simplify \(1,000^{23}\), we first express \(1,000\) as a power of \(10\):

\[
1,000 = 10^3
\]

Now, we can rewrite \(1,000^{23}\) using this conversion:

\[
1,000^{23} = (10^3)^{23}
\]

When we exponentiate a power, we multiply the exponents:

\[
(10^3)^{23} = 10^{3 \cdot 23} = 10^{69}
\]

The result is \(10^{69}\).

Now, let's evaluate what each person said:

1. **Charles** says the simplification is \(10\). This is incorrect.
2. **Zayeer** says the simplification is \(1,000\). This is also incorrect.
3. **Kali** says the simplification is \(100\). This is also incorrect.

So, none of them have the correct simplification. The correct value is \(10^{69}\).