Question

Which expression leaves you with the smallest number on the number line?

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(1 point)
Responses

10⁵ ⋅10−⁴
10 to the 5th power times 10 to the negative 4 power

(10−²)−²
open paren 10 to the negative 2 power close paren to the negative 2 power

10⁸ / 10⁸
the fraction with numerator 10 to the 8th power and denominator 10 to the 8th power

10⁸/10¹⁰

Answer 1

To determine which expression yields the smallest number, let's evaluate each expression step by step.

1. **\( 10^5 \cdot 10^{-4} \)**:
\[
10^5 \cdot 10^{-4} = 10^{5-4} = 10^1 = 10
\]

2. **\( (10^{-2})^{-2} \)**:
\[
(10^{-2})^{-2} = 10^{-2 \cdot -2} = 10^4 = 10,000
\]

3. **\( \frac{10^8}{10^8} \)**:
\[
\frac{10^8}{10^8} = 10^{8-8} = 10^0 = 1
\]

4. **\( \frac{10^8}{10^{10}} \)**:
\[
\frac{10^8}{10^{10}} = 10^{8-10} = 10^{-2} = 0.01
\]

Now we compare the results:
- \( 10^5 \cdot 10^{-4} = 10 \)
- \( (10^{-2})^{-2} = 10,000 \)
- \( \frac{10^8}{10^8} = 1 \)
- \( \frac{10^8}{10^{10}} = 0.01 \)

The smallest number on the number line among these results is:
\[
\frac{10^8}{10^{10}} = 0.01
\]

So, the expression that leaves you with the smallest number on the number line is:
\[
\frac{10^8}{10^{10}}
\]