Question

omplete the table below.(4 points)
Rational Exponent Form Root Form Simplify
81−−√4
12112

Answer 1

To complete the table, we will convert between rational exponent form and root form, and then simplify the expressions.

### Table:

| Rational Exponent Form | Root Form | Simplify |
|------------------------|-----------|-----------------|
| \( 81^{\frac{1}{4}} \) | \( \sqrt[4]{81} \) | \( 3 \) |
| \( 121^{\frac{1}{2}} \) | \( \sqrt{121} \) | \( 11 \) |

### Explanation:
1. **For \( 81^{\frac{1}{4}} \)**:
- Root Form: The fourth root of 81 can be written as \( \sqrt[4]{81} \).
- Simplification: Since \( 81 = 3^4 \), we find \( \sqrt[4]{81} = \sqrt[4]{3^4} = 3 \).

2. **For \( 121^{\frac{1}{2}} \)**:
- Root Form: This is the square root of 121, which can be written as \( \sqrt{121} \).
- Simplification: Since \( 121 = 11^2 \), we have \( \sqrt{121} = 11 \).

Thus, the table is complete with both the rational exponent forms, root forms, and their simplifications filled in.