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

Let's simplify the expression \( 1,000^{23} \).

First, express 1,000 in terms of powers of 10:

\[
1,000 = 10^3
\]

Now, we can substitute this into the original expression:

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

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

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

Now, we need to evaluate \( 10^{69} \). This represents a very large number, specifically a 1 followed by 69 zeros.

None of the provided answers (10, 1,000, or 100) represent the correct simplification of \( 1,000^{23} \). The correct value is \( 10^{69} \).

So, all three (Charles, Zayeer, and Kali) are incorrect.