Question

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

options:

10^5 ⋅ 10^−4 ⋅ 10^−5

10^15 over 10^−3

(10^2)^8

10^8 over 10^18

Answer 1

Let's evaluate each expression to determine which one yields the largest number.

1. **Expression: \(10^5 \cdot 10^{-4} \cdot 10^{-5}\)**
Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\):
\[
10^5 \cdot 10^{-4} \cdot 10^{-5} = 10^{5 - 4 - 5} = 10^{-4}
\]

2. **Expression: \(\frac{10^{15}}{10^{-3}}\)**
Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\):
\[
\frac{10^{15}}{10^{-3}} = 10^{15 - (-3)} = 10^{15 + 3} = 10^{18}
\]

3. **Expression: \((10^2)^8\)**
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\):
\[
(10^2)^8 = 10^{2 \cdot 8} = 10^{16}
\]

4. **Expression: \(\frac{10^8}{10^{18}}\)**
Again, using the property of exponents:
\[
\frac{10^8}{10^{18}} = 10^{8 - 18} = 10^{-10}
\]

Now we summarize the evaluated results:
- Expression 1: \(10^{-4}\)
- Expression 2: \(10^{18}\)
- Expression 3: \(10^{16}\)
- Expression 4: \(10^{-10}\)

Comparing these values, \(10^{18}\) is the largest number on the number line.

Thus, the expression that leaves you with the largest number is:
\[
\boxed{\frac{10^{15}}{10^{-3}}}
\]