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# Chapter 7

### Powers

Powering x^n
Base the variable, x for example
Exponent the power, n for example
Identity Function x^1
2nd Power, Squaring x^2
Cubing x^3
Product of Powers b^m x b^n = b^m+n
Power of a Power (b^m)^n = b^mXn
Power of a Product (ab)^m = a^m x b^m
Quotient of Powers b^m/b^n = b^m-n
Power of a Quotient (a/b)^m = a^m/b^m
Zero Exponent b^0 = 1
Negative Exponent b^-n = 1/b^n
Compounding interest earns interest each year
Annual Compound Interest Formula A=P(1+r)^t
General Compound Interest Formula A=P(1+t/n)^nt
Constant Ratio constant multiplier, r
Explicit Formula for a Geometric Sequence Gn=G1(r)^n-1
B is the nth root of x only if b^n=x
1/n Exponent Theorem when x is greater than or equal to 0 and n is an integer greater than one, 1/x^n is an nth root of x
Number of Real Roots POSITIVE REAL NUMBERS: n is even = 2 real nth roots n is odd = 1 real nth root NEGATIVE REAL NUMBERS: n is even = 0 real nth roots n is odd = 1 real nth root
Created by: acaforever