An exponent is a small number written above and to the right of another number (called the base) that tells you how many times to multiply that base by itself.

Quick definition

  • In the expression ana^nan,
    • aaa is the base ,
    • nnn is the exponent (or power).
  • For example, in 535^353, the exponent 3 means 5×5×5=1255\times 5\times 5=1255×5×5=125.

Simple examples

  • 24=2×2×2×2=162^4=2\times 2\times 2\times 2=1624=2×2×2×2=16.
  • 82=8×8=648^2=8\times 8=6482=8×8=64.

Why exponents matter

Exponents are a compact way to write repeated multiplication, which is especially handy for very large or very small numbers (like in scientific notation or computer science). They’re also central to algebra, where you simplify expressions using rules such as:

  • am⋅an=am+na^m\cdot a^n=a^{m+n}am⋅an=am+n (product of powers),
  • (am)n=am⋅n(a^m)^n=a^{m\cdot n}(am)n=am⋅n (power of a power), and
  • a0=1a^0=1a0=1 for any nonzero base aaa.

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