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)
Responses

Charles
Charles

Zayeer
Zayeer

none of them
none of them

Kali

Answer 1

To simplify \( 1,000^{23} \), we first rewrite \( 1,000 \) in terms of base \( 10 \):

\[
1,000 = 10^3
\]

Now, we can raise \( 1,000 \) to the power of \( 23 \):

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

Using the power of a power property of exponents, we multiply the exponents:

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

Now we can see what each person claimed:

- Charles claims \( 1,000^{23} = 10 \) (incorrect)
- Zayeer claims \( 1,000^{23} = 1,000 \) (incorrect)
- Kali claims \( 1,000^{23} = 100 \) (incorrect)

Since the correct simplification is \( 10^{69} \), the answer is:

**none of them**