define the laws of exponents
http://www.mathsisfun.com/algebra/exponent-laws.html
The laws of exponents, also known as the rules of exponents, are a set of rules that govern the manipulation and simplification of exponential expressions. These laws are important in algebra and provide a way to simplify and solve problems involving large or small numbers raised to different powers.
There are six main laws of exponents:
1. Product law: When multiplying two exponential expressions with the same base, we can add their exponents. For example, a^m * a^n = a^(m + n).
2. Quotient law: When dividing two exponential expressions with the same base, we can subtract their exponents. For example, a^m / a^n = a^(m - n).
3. Power of a power law: When raising an exponential expression to another exponent, we can multiply the exponents. For example, (a^m)^n = a^(m * n).
4. Power of a product law: When raising a product of two or more exponential expressions to an exponent, we can distribute the exponent to each term within the parentheses. For example, (ab)^n = a^n * b^n.
5. Power of a quotient law: When raising a quotient of two exponential expressions to an exponent, we can distribute the exponent to both the numerator and denominator. For example, (a/b)^n = (a^n) / (b^n).
6. Zero exponent law: Any non-zero number raised to the power of zero is equal to 1. For example, a^0 = 1, where "a" is any non-zero number.
By applying these laws, we can simplify complex exponential expressions and solve equations involving exponents. It is essential to understand and use these laws effectively when working with exponential functions and equations.