Simplify each of the
`(root(4)243)/(root(4)3)`

Answer

To simplify the expression \((\sqrt[4]{243}) / (\sqrt[4]{3})\), we can follow these steps:

1. **Rewrite the expression using exponents**:
The fourth root can be expressed as raising to the power of \(1/4\). Therefore, we can rewrite the expression as:
\[ \frac{243^{1/4}}{3^{1/4}} \]

2. **Combine the fractions**:
Since both the numerator and the denominator are raised to the same power, we can combine them:
\[ = \left(\frac{243}{3}\right)^{1/4} \]

3. **Simplify the fraction inside the root**:
Now, we simplify \(\frac{243}{3}\):
\[ 243 \div 3 = 81 \]
So, we have:
\[ = 81^{1/4} \]

4. **Rewrite 81 as a power of 3**:
We know that \(81 = 3^4\). Therefore, we can rewrite the expression as:
\[ = (3^4)^{1/4} \]

5. **Apply the power of a power rule**:
When raising a power to another power, we multiply the exponents:
\[ = 3^{4 \cdot \frac{1}{4}} = 3^1 \]

6. **Final result**:
Thus, the simplified expression is:
\[ = 3 \]