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

Question

. 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.