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Answer :
To simplify the radical expression [tex]\(\sqrt[4]{81 x^4}\)[/tex], follow these steps:
1. Recognize the parts of the expression:
- 81 is a constant number.
- [tex]\(x^4\)[/tex] is a variable raised to the fourth power.
2. Simplify the constant part ([tex]\(81\)[/tex]):
- Find the fourth root of 81. Since [tex]\(81 = 3^4\)[/tex], the fourth root of 81 is 3.
3. Simplify the variable part ([tex]\(x^4\)[/tex]):
- Take the fourth root of [tex]\(x^4\)[/tex]. The fourth root of [tex]\(x^4\)[/tex] is [tex]\(x^{4/4} = x^1 = x\)[/tex].
4. Combine the results:
- Multiply the simplified constant and variable parts together: [tex]\(3 \times x = 3x\)[/tex].
So, the simplified expression is [tex]\(3x\)[/tex].
1. Recognize the parts of the expression:
- 81 is a constant number.
- [tex]\(x^4\)[/tex] is a variable raised to the fourth power.
2. Simplify the constant part ([tex]\(81\)[/tex]):
- Find the fourth root of 81. Since [tex]\(81 = 3^4\)[/tex], the fourth root of 81 is 3.
3. Simplify the variable part ([tex]\(x^4\)[/tex]):
- Take the fourth root of [tex]\(x^4\)[/tex]. The fourth root of [tex]\(x^4\)[/tex] is [tex]\(x^{4/4} = x^1 = x\)[/tex].
4. Combine the results:
- Multiply the simplified constant and variable parts together: [tex]\(3 \times x = 3x\)[/tex].
So, the simplified expression is [tex]\(3x\)[/tex].
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