Express the following in the simplest form :
`root(4)(root(5)(1048576))`

Answer

To simplify the expression \( \sqrt[4]{\sqrt[5]{1048576}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt[4]{\sqrt[5]{1048576}} \]
This can be rewritten using exponent notation:
\[ (1048576)^{\frac{1}{5}}^{\frac{1}{4}} = (1048576)^{\frac{1}{20}} \]

### Step 2: Factor \( 1048576 \)
Next, we need to express \( 1048576 \) as a power of \( 2 \). We can find that:
\[ 1048576 = 2^{20} \]
This can be verified by calculating \( 2^{20} \) or by factoring \( 1048576 \) into its prime factors.

### Step 3: Substitute back into the expression
Now we substitute \( 1048576 \) in our expression:
\[ (2^{20})^{\frac{1}{20}} \]

### Step 4: Simplify the exponent
Using the power of a power property \( (a^m)^n = a^{m \cdot n} \), we simplify:
\[ 2^{20 \cdot \frac{1}{20}} = 2^1 = 2 \]

### Final Answer
Thus, the simplest form of the expression \( \sqrt[4]{\sqrt[5]{1048576}} \) is:
\[ \boxed{2} \]