Let's evaluate each expression to determine which one yields the largest number.
-
Expression: \(10^5 \cdot 10^{-4} \cdot 10^{-5}\)
Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\): \[ 10^5 \cdot 10^{-4} \cdot 10^{-5} = 10^{5 - 4 - 5} = 10^{-4} \] -
Expression: \(\frac{10^{15}}{10^{-3}}\)
Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\): \[ \frac{10^{15}}{10^{-3}} = 10^{15 - (-3)} = 10^{15 + 3} = 10^{18} \] -
Expression: \((10^2)^8\)
Using the property of exponents that states \((a^m)^n = a^{m \cdot n}\): \[ (10^2)^8 = 10^{2 \cdot 8} = 10^{16} \] -
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: \[ \boxed{\frac{10^{15}}{10^{-3}}} \]
1 answer