Exponent Rules Calculator

Work out exponent rules instantly with clear inputs, formula shown and shareable results.

About Exponent Rules Calculator

The index laws all follow from counting factors: multiplying powers of the same base adds the exponents, dividing subtracts them, and raising a power to a power multiplies them.

Formulas

Product rule

bᵐ × bⁿ = bᵐ⁺ⁿ

Quotient rule

bᵐ ÷ bⁿ = bᵐ⁻ⁿ

Power rule

(bᵐ)ⁿ = bᵐⁿ

Worked example

With the default values below, Exponent Rules Calculator returns bᵐ × bⁿ = bᵐ⁺ⁿ of 256.000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base bminimum 0: 2
First exponent m: 5
Second exponent n: 3

Results

bᵐ × bⁿ = bᵐ⁺ⁿ: 256.000000
bᵐ ÷ bⁿ = bᵐ⁻ⁿ: 4.00000000
(bᵐ)ⁿ = bᵐⁿ: 32,768.000000
b⁰: 1

Step by step

1Values used
2Product rule
3Quotient rule
4Power rule
5bᵐ × bⁿ = bᵐ⁺ⁿ= 256.000000
6bᵐ ÷ bⁿ = bᵐ⁻ⁿ= 4.00000000
7(bᵐ)ⁿ = bᵐⁿ= 32,768.000000
8b⁰= 1

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For b = 2, m = 5, n = 3?

2⁸ = 256, 2² = 4 and 2¹⁵ = 32768.

Why is b⁰ always 1?

Because bᵐ ÷ bᵐ = bᵐ⁻ᵐ = b⁰, and any non-zero number divided by itself is 1.