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

Question

 

(1 point)
Responses

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

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

101510−3
the fraction with numerator 10 to the 15th power and denominator 10 to the negative 3 power

1081018
the fraction with numerator 10 to the 8th power and denominator 10 to the 18th power
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Answer 1

Let's evaluate each expression to determine which leaves the largest number on the number line.

1. \( 105 \cdot 10^{-4} \cdot 10^{-5} \)
   We can simplify this:
   \[ 105 \cdot 10^{-4} \cdot 10^{-5} = 105 \cdot 10^{-9} \] This is equivalent to \( 1.05 \times 10^{2} \cdot 10^{-9} = 1.05 \times 10^{-7} \).

2. \( (10^2)^8 \)
   We can simplify this using the exponent rule \( (a^m)^n = a^{mn} \):
   \[ (10^2)^8 = 10^{2 \cdot 8} = 10^{16} \]

3. \( \frac{10^{15}}{10^{-3}} \)
   We can simplify this using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):
   \[ \frac{10^{15}}{10^{-3}} = 10^{15 - (-3)} = 10^{15 + 3} = 10^{18} \]

4. \( \frac{10^8}{10^{18}} \)
   We can simplify this using the property of exponents:
   \[ \frac{10^8}{10^{18}} = 10^{8 - 18} = 10^{-10} \]

Now we compare the results:

1. \( 105 \cdot 10^{-4} \cdot 10^{-5} = 1.05 \times 10^{-7} \)
2. \( (10^2)^8 = 10^{16} \)
3. \( \frac{10^{15}}{10^{-3}} = 10^{18} \)
4. \( \frac{10^8}{10^{18}} = 10^{-10} \)

The largest number on the number line is \( 10^{18} \).

Therefore, the expression that leaves you with the largest number is \( \frac{10^{15}}{10^{-3}} \).