Integer Exponent
\(2^3 = 2 \times 2 \times 2 = 8\)
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Theory & Formula
Exponentiation is a mathematical operation involving two numbers: the base (a) and the exponent (n).
Exponent rules and properties:
- Positive integer: an = a × a × ... × a (n times)
- Zero exponent: a0 = 1 (where a ≠ 0)
- Negative exponent: a-n = 1 / an
- Fractional exponent: a1/n = n√a (nth root of a)
- Product rule: am × an = am+n
- Power rule: (am)n = amn
\(y = a^n\)
Worked Examples
Negative Exponent
\(2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\)
Fractional Exponent
\(16^{1/2} = \sqrt{16} = 4\)