How is built-in function pow() function different from function math.pow() ? Explain with an example.

Question

Accepted Answer

> [!TLDR]
> Both raise a number to a power, but built-in `pow()` works with exact integers, needs no import and offers a three-argument modular form, while `math.pow()` always converts to float, returns a float, and takes exactly two arguments.

**The idea.** Python has two exponentiation functions because they serve different domains: the **built-in** `pow()` is general-purpose (integer-exact, and with the `pow(base, exp, mod)` form used in number theory), whereas `math.pow()` belongs to the C-style floating-point library — everything in the `math` module speaks float.

```python
import math

print(pow(2, 10))            # built-in: int result
print(math.pow(2, 10))       # math module: float result
print(pow(5, 2, 3))          # three-argument form: (5**2) % 3
```

**Expected output**

```
1024
1024.0
1
```

**The differences, side by side**

| | built-in `pow()` | `math.pow()` |
|---|---|---|
| Import needed | no | yes (`import math`) |
| `pow(2, 10)` | `1024` (int, exact) | `1024.0` (float) |
| Return type | int for int args, float otherwise | **always** float |
| Third argument | yes — `pow(a, b, m)` = a to the power b, modulo m | no — `TypeError` |
| Very large integers | exact (unlimited precision) | rounded to float precision |

- The three-argument call `pow(5, 2, 3)` computes 5² = 25, then 25 mod 3 = **1**, efficiently — handy in cryptography-style computations. `math.pow(5, 2, 3)` raises `TypeError: math.pow() takes exactly 2 arguments (3 given)`. …

$x$	$\lfloor x \rfloor$	$\lceil x \rceil$
2.1	2	3
2.9	2	3
-2.1	-3	-2
-2.9	-3	-2
4	4	4

	built-in `pow()`	`math.pow()`
Import needed	no	yes (`import math`)
`pow(2, 10)`	`1024` (int, exact)	`1024.0` (float)
Return type	int for int args, float otherwise	always float
Third argument	yes — `pow(a, b, m)` = a to the power b, modulo m	no — `TypeError`
Very large integers	exact (unlimited precision)	rounded to float precision

Q.How is built-in function pow() function different from function math.pow() ? Explain with an example.

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Q.How is built-in function pow() function different from function math.pow() ? Explain with an example.

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