Question

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

A. (10^-2)^-7
B. 10^8/10^14
C. 10^18/10^8
D. 10^5 * 10^-4 * 10^11

Answer 1

To determine which expression yields the largest number on the number line, let's simplify each option:

**A. \((10^{-2})^{-7}\)**

Using the power of a power property, we have:
\[
(10^{-2})^{-7} = 10^{-2 \cdot -7} = 10^{14}
\]

**B. \(\frac{10^8}{10^{14}}\)**

Using the quotient property, we simplify:
\[
\frac{10^8}{10^{14}} = 10^{8 - 14} = 10^{-6}
\]

**C. \(\frac{10^{18}}{10^8}\)**

Using the quotient property:
\[
\frac{10^{18}}{10^{8}} = 10^{18 - 8} = 10^{10}
\]

**D. \(10^5 \cdot 10^{-4} \cdot 10^{11}\)**

Using the product property, we combine the exponents:
\[
10^5 \cdot 10^{-4} \cdot 10^{11} = 10^{5 + (-4) + 11} = 10^{5 - 4 + 11} = 10^{12}
\]

Now we summarize the results:

- A: \(10^{14}\)
- B: \(10^{-6}\)
- C: \(10^{10}\)
- D: \(10^{12}\)

Comparing these, we have:

\[
10^{14} > 10^{12} > 10^{10} > 10^{-6}
\]

The largest expression is A, which is \(10^{14}\).

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

\(\boxed{A}\)