# Multiplying Exponents Calculator

URL: https://speedycalculator.com/calculators/math/multiplying-exponents/
Last updated: 2026-10-30

> The multiplying exponents calculator simplifies aᵐ × bⁿ – adding exponents when the bases match, multiplying bases when the exponents match – and gives the value.

## Inputs

- Operation
- Base a
- Exponent m
- Base b
- Exponent n

## Results

- Simplified
- Value
- Rule
- Each power

## Formula

```
aᵐ × aⁿ = a^(m + n),  aⁿ × bⁿ = (a·b)ⁿ
```

## Explanation

Multiplying powers is a cornerstone of algebra: 2³ × 2⁴ = 2⁷ because you are multiplying seven 2s. The same rules work with negative and fractional exponents and with scientific notation (10⁵ × 10³ = 10⁸).

### How to use the Multiplying Exponents Calculator

- **Operation**
- **Base a**
- **Exponent m**
- **Base b**
- **Exponent n**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Enter both powers. The calculator checks whether the bases or the exponents match and applies the right rule; otherwise it evaluates each power.

## Worked example

Inputs — Operation: Multiply aᵐ × bⁿ; Base a: 2; Exponent m: 3; Base b: 2; Exponent n: 4.

Results — **Simplified = 2⁷**; Value = 128; Rule = Same base: add the exponents: 3 + 4 = 7; Each power = 2³ = 8
2⁴ = 16.

## Key terms

- **Product of powers**: aᵐ·aⁿ = aᵐ⁺ⁿ.

## FAQ

**What is x² × x³?**
x⁵.

**What is 2³ × 3³?**
6³ = 216.

**Can I add exponents with different bases?**
No – 2³ × 3⁴ cannot be written as a single power with an integer base.

**What about negative exponents?**
Same rule: 5² × 5⁻³ = 5⁻¹ = 0.2.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)