To compare \( 4 \cdot 10^1 \) and \( 8 \cdot 10^2 \), we first need to express both numbers in a similar form.
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Calculate \( 4 \cdot 10^1 \): \[ 4 \cdot 10^1 = 4 \cdot 10 = 40 \]
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Calculate \( 8 \cdot 10^2 \): \[ 8 \cdot 10^2 = 8 \cdot 100 = 800 \]
Now, we need to determine how many times larger \( 40 \) is than \( 800 \).
To find how many times larger \( 800 \) is than \( 40 \), use the following formula: \[ \text{Times larger} = \frac{800}{40} \]
Calculating this gives: \[ \frac{800}{40} = 20 \]
Thus, \( 8 \cdot 10^2 \) is \( 20 \) times larger than \( 4 \cdot 10^1 \).
The answer is: 20 times larger.