Exponents
Exponents are a mathematical way to show repeated multiplication of the same number by itself.
An exponent is written as a small number (called the power) above and to the right of a base number, like this:
Base^Exponent = Base • Base • … • Base
Example: (2^3 = 2 • 2 • 2 = 8).
Laws of Exponents
Product Rule: (a^m \times a^n = a^{m+n})
Example: (2^3 • 2^4 = 2^{3+4} = 2^7 = 128).
Quotient Rule: ({a^m}/{a^n} = a^{m-n}) (if (a ≠ 0))
Example: ({5^6}/{5^2} = 5^{6-2} = 5^4 = 625).
Power Rule: ((a^m)^n = a^{mn})
Example: ((3^2)^3 = 3^{2 • 3} = 3^6 = 729).
Zero Exponent: (a^0 = 1) (if (a ≠ 0))
Example: (7^0 = 1)
Negative Exponent: (a^{-n} = {1/{a^n})
Example: (2^{-3} = {1}/{2^3} = 1/8).