Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (0.2)^4 = 0.0016 \)
Solution
To calculate \( (0.2)^4 \), follow these steps:
1. **First Power:**
\[
0.2^1 = 0.2
\]
2. **Second Power:**
\[
0.2^2 = 0.2 \times 0.2 = 0.04
\]
3. **Third Power:**
\[
0.2^3 = 0.04 \times 0.2 = 0.008
\]
4. **Fourth Power:**
\[
0.2^4 = 0.008 \times 0.2 = 0.0016
\]
So,
\[
(0.2)^4 = 0.0016
\]
**Final Answer:**
\( (0.2)^{4} = 0.0016 \)
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Simplify this solution Beyond the Answer
First, let’s tackle \( (0.2)^{4} \) together! When you raise 0.2 to the power of 4, you’re actually multiplying 0.2 by itself four times: \( 0.2 \times 0.2 \times 0.2 \times 0.2 \). This equals \( 0.016 \). It’s a fun little exercise in understanding how decimal places shift with powers! Now, why does this matter? Well, in real-world terms, powers of numbers (especially decimals) can pop up in many places, like calculating probabilities in games of chance, measuring areas, or figuring out discounts in shopping. For example, if you have a 20% off sale, calculating the final price can often involve similar fractional representations!
