`root(3)(root(3)(a^(3)))` is equal to

Options

A. a
B. 1
C. `a^(1//3)`
D. `a^(3)`

Answer

To solve the expression \( \sqrt[3]{\sqrt[3]{a^3}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \sqrt[3]{\sqrt[3]{a^3}} \]
This can be rewritten as:
\[ \sqrt[3]{(a^3)^{1/3}} \]

### Step 2: Apply the power of a power rule
Using the power of a power rule, which states that \( (x^m)^n = x^{m \cdot n} \), we can simplify:
\[ \sqrt[3]{(a^3)^{1/3}} = (a^3)^{1/3} = a^{3 \cdot \frac{1}{3}} = a^1 \]

### Step 3: Simplify the expression
Now, we simplify \( a^1 \):
\[ a^1 = a \]

### Final Answer
Thus, the expression \( \sqrt[3]{\sqrt[3]{a^3}} \) is equal to:
\[ a \]

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