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# Bash Exponentiation
The `**` operator in Bash serves two distinct technical functions depending on its execution context: it acts as the **exponentiation operator** within arithmetic evaluation, and as the **recursive wildcard (globstar)** within pathname expansion.
## 1. Arithmetic Expansion (Exponentiation)
Within arithmetic contexts—such as `$((...))`, `((...))`, the `let` builtin, or variables typed with `declare -i`—the `**` token functions as a right-associative exponentiation operator. It evaluates the left operand (base) raised to the power of the right operand (exponent).
Because Bash arithmetic is strictly limited to fixed-width integers (typically 64-bit signed integers), the `**` operator does not support floating-point operands. Negative exponents are invalid and will trigger an explicit error (e.g., `bash: exponent less than 0`), aborting the arithmetic evaluation. Operations exceeding the maximum integer limit will silently overflow.
Unlike other arithmetic operators, Bash does not implement a compound exponentiation assignment operator (`**=`). The result of an exponentiation must be explicitly assigned back to a variable.
```bash theme={"dark"}
# Standard arithmetic expansion syntax
result=$(( base ** exponent ))
# Explicit assignment within arithmetic context
(( base = base ** exponent ))
# Builtin evaluation syntax
let "result = base ** exponent"
```
## 2. Pathname Expansion (Globstar)
During pathname expansion (globbing), `**` acts as a recursive matching operator. By default, this behavior is disabled and must be explicitly activated using the `shopt` builtin to set the `globstar` option (introduced in Bash 4.0).
When `globstar` is enabled, the `**` token matches all files, as well as zero or more directories and subdirectories. The evaluation engine traverses the directory tree recursively. Since Bash 4.3, the `**` operator explicitly does *not* traverse symbolic links that point to directories. This is a vital safety mechanism designed to prevent infinite recursion loops during directory tree traversal.
Crucially, `**` does not match hidden files or traverse into hidden directories (those starting with `.`) unless the `dotglob` shell option is explicitly enabled via `shopt -s dotglob`.
* If `**` appears alone, it matches all non-hidden files and directories in the current directory tree.
* If `**` is followed by a slash (`**/`), the expansion is strictly restricted to directories and subdirectories, excluding standard files.
* If `**` is part of a larger pattern (e.g., `**/*.txt`), it applies the suffix pattern to all files and directories discovered during the recursive traversal.
```bash theme={"dark"}
# Activation requirements
shopt -s globstar
shopt -s dotglob # Optional: required to match and traverse hidden files/directories
# Syntax variations (passed as arguments to a command to prevent execution errors)
echo ** # Expands to all files and zero or more directories recursively
echo **/ # Expands strictly to zero or more directories recursively
echo **/* # Expands to all files and directories within the recursive directory tree
echo **/pattern # Expands to files/directories matching 'pattern' in the current directory and all subdirectories
```
*Note: If the `globstar` option is disabled, Bash treats `**` identically to a single `*` (standard wildcard), matching only files and directories in the immediate current working directory.*
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