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 \(10^{69}\).