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?(1 point)

Answer 1

To evaluate \( 1,000^{23} \), we first rewrite 1,000 in terms of powers of 10. We know:

\[
1,000 = 10^3.
\]

Now, we raise this to the power of 23:

\[
1,000^{23} = (10^3)^{23} = 10^{3 \cdot 23} = 10^{69}.
\]

So the correct simplification of \( 1,000^{23} \) is \( 10^{69} \).

Now let's analyze what each of the individuals claimed:

- Charles said \( 1,000^{23} = 10 \). This is incorrect.
- Zayeer said \( 1,000^{23} = 1,000 \). This is also incorrect.
- Kali said \( 1,000^{23} = 100 \). This is incorrect as well.

None of them are correct. The correct simplified value is \( 10^{69} \).