Question

which expression is equivalent to 1,000+196?

Answers,
10 to the power of 2 + 7 dot operator symbol 28,
10 to the power of 3 + 14 to the power of 2,
100 to the power of 3 + 7 dot operator symbol 28,
or 100 to the power of 2 + 14 to the power of 2?

Answer 1

To find an expression equivalent to \( 1,000 + 196 \):

First, calculate the sum:
\[
1,000 + 196 = 1,196
\]

Next, let's evaluate each given option.

1. **Option 1:** \( 10^2 + 7 \cdot 28 \)
\[
10^2 = 100 \quad \text{and} \quad 7 \cdot 28 = 196 \quad \Rightarrow \quad 100 + 196 = 296
\]

2. **Option 2:** \( 10^3 + 14^2 \)
\[
10^3 = 1,000 \quad \text{and} \quad 14^2 = 196 \quad \Rightarrow \quad 1,000 + 196 = 1,196
\]

3. **Option 3:** \( 100^3 + 7 \cdot 28 \)
\[
100^3 = 1,000,000 \quad \text{and} \quad 7 \cdot 28 = 196 \quad \Rightarrow \quad 1,000,000 + 196 = 1,000,196
\]

4. **Option 4:** \( 100^2 + 14^2 \)
\[
100^2 = 10,000 \quad \text{and} \quad 14^2 = 196 \quad \Rightarrow \quad 10,000 + 196 = 10,196
\]

Out of these calculations, the only expression that equals \( 1,196 \) is:

**Option 2:** \( 10^3 + 14^2 \)

Thus, the equivalent expression is \( 10^3 + 14^2 \).