Question

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

10 to the eighth power / 10 to the fourteenth power
10 to the fifth power times 10 to the negative fourth power times 10 to the eleventh power
10 to the eighteenth power / 10 to the eighth power
(10 to the negative second power) to the negative seventh power

Answer 1

Let's simplify each given expression to find out which one results in the largest number.

1. **First Expression:**
\[
\frac{10^8}{10^{14}} = 10^{8 - 14} = 10^{-6}
\]
This equals \(0.000001\).

2. **Second Expression:**
\[
10^5 \times 10^{-4} \times 10^{11} = 10^{5 - 4 + 11} = 10^{12}
\]
This equals \(1,000,000,000,000\).

3. **Third Expression:**
\[
\frac{10^{18}}{10^8} = 10^{18 - 8} = 10^{10}
\]
This equals \(10,000,000,000\).

4. **Fourth Expression:**
\[
(10^{-2})^{-7} = 10^{-2 \times -7} = 10^{14}
\]
This equals \(100,000,000,000,000\).

Now we compare the results:
- First Expression: \(10^{-6} = 0.000001\)
- Second Expression: \(10^{12} = 1,000,000,000,000\)
- Third Expression: \(10^{10} = 10,000,000,000\)
- Fourth Expression: \(10^{14} = 100,000,000,000,000\)

Among these, the largest number is \(10^{14}\), which comes from the fourth expression: \((10^{-2})^{-7}\).

Thus, the expression that leaves you with the largest number on the number line is:
\[
(10^{-2})^{-7}
\]