Question
3. Which expression is equal to \( 3^{4} \) ? A \( \sqrt[4]{3} \) B \( \sqrt[4]{81} \) C 12 D \( 9^{2} \)
Ask by Williams Olson. in Canada
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct answer is D \( 9^{2} \).
Solution
To determine which expression is equal to \( 3^{4} \), we can evaluate each option:
1. **Option A: \( \sqrt[4]{3} \)**
This is equal to \( 3^{1/4} \), which is not equal to \( 3^{4} \).
2. **Option B: \( \sqrt[4]{81} \)**
We know that \( 81 = 3^{4} \). Therefore,
\[
\sqrt[4]{81} = \sqrt[4]{3^{4}} = 3^{4/4} = 3^{1} = 3
\]
This is not equal to \( 3^{4} \).
3. **Option C: 12**
This is simply a number and does not equal \( 3^{4} \).
4. **Option D: \( 9^{2} \)**
We know that \( 9 = 3^{2} \). Therefore,
\[
9^{2} = (3^{2})^{2} = 3^{2 \cdot 2} = 3^{4}
\]
This is equal to \( 3^{4} \).
Thus, the correct answer is **D \( 9^{2} \)**.
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Simplify this solution Bonus Knowledge
To find which expression is equal to \( 3^{4} \), we can simplify the options. First, \( 3^4 = 81 \), so we can look for an expression that equals \( 81 \). Option B, \( \sqrt[4]{81} \), can be simplified: since \( 81 = 3^4 \), taking the fourth root gives us \( 3 \), not \( 81 \). For option D, \( 9^2 \) can be rewritten as \( (3^2)^2 = 3^{2 \cdot 2} = 3^4 \), which does equal \( 81 \). Therefore, the correct answer is option D, \( 9^{2} \). So, the final answer is D \( 9^{2} \).
