Understanding Exponents and Roots
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. It is written as $x^y$ and is read as "x to the power of y".
Power ($x^y$)
The exponent represents how many times the base is used as a factor in multiplication.
Example: 23 = 2 × 2 × 2 = 8
Roots ($\sqrt[y]{x}$)
A root is the inverse operation of exponentiation. The N-th root of a number x is a number r which, when raised to the power n, equals x ($r^n = x$).
Example: 3√8 = 2 (because 2 × 2 × 2 = 8)
Special Cases
- Exponent 0: Any non-zero number raised to the power of 0 is 1.
- Exponent 1: Any number raised to the power of 1 is itself.
- Negative Exponents: $x^{-n}$ is equal to $1/x^n$. For example, $2^{-3} = 1/8 = 0.125$.