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

Question

(1 point)
Responses

1081018
the fraction with numerator 10 to the 8th power and denominator 10 to the 18th power

(102)8
open paren 10 squared close paren to the 8th power

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

10(15)/10(−3)

Answer 1

To determine which expression leaves you with the largest number on the number line, we can simplify each option:

1. \( \frac{10^8}{10^{18}} \): \[ \frac{10^8}{10^{18}} = 10^{8 - 18} = 10^{-10} \approx 0.0000000001 \]

2. \( (10^2)^8 \): \[ (10^2)^8 = 10^{2 \times 8} = 10^{16} \]

3. \( 10^5 \cdot 10^{-4} \cdot 10^{-5} \): \[ 10^5 \cdot 10^{-4} \cdot 10^{-5} = 10^{5 - 4 - 5} = 10^{-4} = 0.0001 \]

4. \( \frac{10^{15}}{10^{-3}} \): \[ \frac{10^{15}}{10^{-3}} = 10^{15 - (-3)} = 10^{15 + 3} = 10^{18} \]

Now we can compare the results:

1. \( 10^{-10} \approx 0.0000000001 \)
2. \( 10^{16} \)
3. \( 10^{-4} = 0.0001 \)
4. \( 10^{18} \)

The largest value is clearly \( 10^{18} \).

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

\( \frac{10^{15}}{10^{-3}} \)