High School

Simplify the following radical expression:

[tex]\sqrt[4]{81 x^4}[/tex]

A. [tex]3x[/tex]
B. [tex]9x[/tex]
C. [tex]3x^4[/tex]
D. [tex]9x^4[/tex]

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].