Question

Which expression leaves you with the largest number on the number line?(1 point)
Responses

105⋅10−4⋅1011
10 to the 5th power times 10 to the negative 4 power times 10 to the 11th power

1081014
the fraction with numerator 10 to the 8th power and denominator 10 to the 14th power

(10−2)−7
open paren 10 to the negative 2 power close paren to the negative 7 power

1018108

Answer 1

To find which expression leaves you with the largest number, let's evaluate each of the expressions step by step.

1. **\( 10^5 \cdot 10^{-4} \cdot 10^{11} \)**:
\[
10^5 \cdot 10^{-4} \cdot 10^{11} = 10^{(5 - 4 + 11)} = 10^{12}
\]

2. **\(\frac{10^8}{10^{14}}\)**:
\[
\frac{10^8}{10^{14}} = 10^{(8 - 14)} = 10^{-6}
\]

3. **\((10^{-2})^{-7}\)**:
\[
(10^{-2})^{-7} = 10^{(-2 \cdot -7)} = 10^{14}
\]

4. **\(10^{18} \cdot 10^{8}\)**:
\[
10^{18} \cdot 10^{8} = 10^{(18 + 8)} = 10^{26}
\]

Now, let's compare the results:

- The first expression evaluates to \(10^{12}\).
- The second expression evaluates to \(10^{-6}\).
- The third expression evaluates to \(10^{14}\).
- The fourth expression evaluates to \(10^{26}\).

Among these, \(10^{26}\) is the largest number.

Therefore, the expression that leaves you with the largest number on the number line is:

**\(10^{18} \cdot 10^{8}\)**.