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
none of them
none of them
Zayeer
Zayeer
Kali

Answer 1

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

\[
1,000 = 10^3
\]

Now, substituting this into the expression \(1,000^{23}\):

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

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

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

Now, let's convert \(10^{69}\) back into a decimal form:

\[
10^{69} = 1\underbrace{00\ldots0}_{69 \text{ zeros}}
\]

This shows that \(1,000^{23} = 10^{69}\), and thus it cannot be simply represented as \(10\), \(1,000\), or \(100\).

Given this, none of the answers provided (Charles: 10, Zayeer: 1,000, Kali: 100) are correct.

So, the answer is **none of them**.