Exponents calculator or converter

Online exponents calculator with negative numbers support and steps.

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Exponents laws and rules and how to apply these rules.

When exponents that share the same base are multiplied, the exponents are added. When an exponent is negative, the negative sign is removed by reciprocating the base and raising it to the positive exponent. ... When exponents are raised to another exponent, the exponents are multiplied.

The exponent formula is:

a ⁿ = a×a×...×a

                    n times

The base a is raised to the power of n, is equal to n times multiplication of a.

For example:

2⁵ = 2×2×2×2×2 = 32

Multiplying exponents

aⁿ ⋅ a^m
= a^n+m

Example: 2³ ⋅ 2⁴ = 2⁽³⁺⁴⁾ = 2⁷ = 128

 

aⁿ ⋅ bⁿ
= (a ⋅ b) ⁿ

Example: 3² ⋅ 4² = (3⋅4)² = 12² = 144

 

Dividing exponents

aⁿ / a^m = a^n-m

Example: 2⁵ / 2³ = 2^(5-3) = 2² = 4

 

aⁿ / bⁿ = (a / b) ⁿ

Example: 8² / 2² = (8/2⁾² = 4² = 16

 

Power of exponent

(aⁿ)^m = a^n⋅m

Example: (2³)⁴ = 2^{(3 ⋅ 4)} = 2¹² = 4096

 

Radical of exponent

^m√(aⁿ) = a^n/m

Example: ²√(2⁶) = 2^{(6 / 2)} = 2³ = 8

 

Negative exponent

a ^-n = 1 / a ⁿ

Example: 2^-3 = 1 / 2³ = 1 / 8 = 0.125

 

Zero exponent

a ⁰ = 1

Example: 4⁰ = 1

What is an exponent?

Exponentiation is a mathematical operation, written as an, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.