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Lecture

# LEC 1: Review of high school material

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http://www.purplemath.com/modules/exponent.htm
2^3 - the 2 is the base, the 3 is the exponent, the whole expression is a power.
(-4)^3 = (-4)(-4)(-4)
-4^3 = -4 x 4 x 4
LAW OF EXPONENTS
Law of Exponent for Multiplication: When multiplying powers with equal bases, add the
exponents.
a^m x a^n = a^m+n
-5^4 x 5 = -(5^4+1) = -5^5
Law of Exponent for Division: When dividing powers with equal bases, subtract the
exponents.
a^m / a^n = a^m-n
Law of Exponent for Powers: When raising a power to an exponent, multiply the inner
exponent by the outer exponent.
(a^m)^n = a^mn
Law of Exponent for Power of products- when raising a product to a power, place the
exponent of the product on each factor
(xy)3 = (xy)(xy)(xy) = x3y3
Law of Exponents for Powers of quotent- when raising a quotient to a power, place
the exponent of the quotient on each of the terms.
(x/y)3 = (x/y)(x/y)(x/y) = x3/y3
ZERO AND NEGATIVE EXPONENTS
Zero Exponents- x^0 is 1 for all numbers except for 0^0, which is undefined.
Negative Exponents- x^ -a = 1/ x^a x^a = 1/ x^ -a
x ^ 1/n = n root of x