ZovaTool

Exponent Calculator

Result

2^10
1024
Scientific
1.024000e+3
Log₂
10
1 / value
0.000977
n-th root verify
2
ln(a)·n (for e^x form)
6.931472

Expansion

2^10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

Powers of 2

2^0
1
2^1
2
2^2
4
2^3
8
2^4
16
2^5
32
2^6
64
2^7
128
2^8
256
2^9
512
2^10
1024

Exponent rules

  • a^m × a^n = a^(m+n)
  • a^m ÷ a^n = a^(m−n)
  • (a^m)^n = a^(m·n)
  • (ab)^n = a^n · b^n
  • a^0 = 1, a ≠ 0
  • a^(−n) = 1/a^n
  • a^(1/n) = ⁿ√a

How to use the Exponent Calculator

  1. Enter a base (a) and an exponent (n).
  2. Result shows a^n in both decimal and scientific notation.
  3. Small integer exponents are expanded as a × a × … for transparency.
  4. Read the property hints for negative and fractional exponents.
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Exponents from scratch

An exponent is a shorthand for repeated multiplication: 2^5 = 2·2·2·2·2 = 32. A negative exponent flips it to a reciprocal: 2^(−3) = 1/2^3 = 1/8.

Fractional exponents are roots: x^(1/2) = √x, x^(1/3) = ∛x. This is what unifies exponents and roots into a single concept.

Useful identities: a^m × a^n = a^(m+n), (a^m)^n = a^(m·n), and a^0 = 1 for any non-zero a.