1.1 Reviewing Exponent Laws
Exponent { base --> a^m <---power }
(i) When multiplying exponents, add the powers: x^a * x^b = x^(a+b)
(ii) When dividing exponents, subtract the powers: x^m/x^n = x^(m-n)
(iii) An exponent to an exponent, multiply the exponents: (a^m)^n = a^mn
(iv) Exponent of products, distribute: (3x)^4 = 3^4 * x^4
(v) Exponent of quotients, distribute: (a/b)^3 = a^3/b^3
(vi) x^0 = 1
(vii) a^-m = 1/a^m
Rational Powers
a^(1/n) = sqare root of "a" for "n" times
Solving Exponential Equations
To solve such equations, you change one or both sides of the equations to exponents with the same base.
e.g. 8^(2x-1) = 16^(x-1)
(2^3)^2x-1 = (2^4)^x-1
2^6x-3 = 2^4x-4
Now, solve 6x-3 = 4x-4.
To factor: 3^(x+2) + 3^x
= 3^x (3^2 +1)
= 3^x(10)
Application: Half Life is the time interval a radio istope occupies to decay to half of its original mass.
Example:
2 kg ----- time -----> 1kg -----time---> 0.5 kg-----time---> 0.25 kg........
2 2(1/2)^1 2(1/2)^2 2(1/2)^3
Formula: AL = Ao (1/2)^t/n
AL = amount left over
Ao = original mass
t= time elapse
h = half life
Examples of questions and solutions: http://www.hts.on.ca/senior/atherrien/MCF3M/Unit1/unit_index.htm