Powers and roots explained simply

In short: A power is repeated multiplication: 2³ = 2 · 2 · 2 = 8. The root is the inverse: √9 = 3, because 3² = 9.

In more detail: In a^n, a is called the base and n the exponent.

In detail

• Laws of exponents: a^m · a^n = a^(m+n); a^m / a^n = a^(m−n); (a^m)^n = a
• Zero exponent: a⁰ = 1 (for a ≠ 0).
• Negative exponent: a^(−n) = 1 / a^n; 2⁻² = 1/4.
• Square root: √a is the non-negative number whose square is a.
• Root as a power: √a = a
• Powers of ten: 10³ = 1000, 10⁻² = 0.01; important for scientific notation.
• Growth: Powers describe rapid growth (exponentielles-wachstum).
• Inverse: Logarithms solve for the exponent (logarithmen-einfach-erklaert).