Exponents, or powers, are fundamental in mathematics, denoting repeated multiplication of a base. This text delves into their properties, including product and quotient rules, and special cases like zero and negative exponents. Rational exponents, which link roots and powers, are also explored. Understanding these concepts is crucial for algebraic simplification and scientific notation, impacting various STEM fields.
Show More
The value being repeatedly multiplied in an exponential expression
The number of times the base is multiplied by itself in an exponential expression
Key rules for simplifying expressions and solving equations involving exponents, including the product of powers, quotient of powers, and power of a power rules
Any base (except zero) raised to the zero power is equal to one
A negative exponent represents the reciprocal of the base raised to the corresponding positive exponent
Fractional exponents correspond to both roots and powers, and can be simplified using the relationship between taking roots and raising to powers
Exponent properties are essential for simplifying and solving algebraic expressions with exponents
A concise way to express very large or small numbers, using a coefficient and a power of 10, commonly used in fields such as physics and engineering
00
Exponentiation example: 5^3
5 raised to the power of 3 equals 125, as 5 is multiplied by itself twice more (5 * 5 * 5).
01
Base in exponentiation
The number being multiplied by itself; in 5^3, the base is 5.
02
Exponential growth and decay relevance
Exponents describe phenomena where quantities increase/decrease rapidly; used in sciences to model population growth, radioactive decay, etc.
