Exponents – F.O.I.L. CHARTS & TABLES
Exponents – F.O.I.L. CHARTS & TABLES
Exponents
Fractional Exponents
xn/b= (b√x)n=b√xn
Division
bm/bn=bm–n
or
= 1/bn–m
Multiplication
bn·bm=bn + m
Negative Exponent Theorem
If x> 0, then
x–n= 1/xn
and
1/x–n=xn
Positive integer
xn= (x·x·x.. .x)
nfactors
Power of a power
(bn)m=bnm
Power of a product
(bc)n=bncn
Power of a fraction
(a/b)n=an/bn
Zero Exponent Theorem
If bis a nonzero real number, then
b^0 = 1Factorial Notation
Factorial notation is the use of a symbol to identify the product of a set of
natural numbers. The symbol looks like this: n!and is called n-factorial.
The equation for n-factorial is:
n!= 1× 2 × 3 ×...×(n– 1) ×n
The equation when nis zero is:
0! = 1F.O.I.L.
A popular method used to multiply two polynomials is called F.O.I.L. It
stands for the order in which the multiplication is done. First, Outside,
Inside, Last, and can often be calculated mentally. Here is an example of
two polynomials multiplied with the F.O.I.L.method:
(x+ 2)(x+ 5)
F (first) = x·x=x^2
O (outside) = 5 · x= 5x
I (inside) = 2 · x= 2x
L (last) = 5 · 2 = 10
So, this multiplies using the F.O.I.L. method as:
(x+ 2)(x+ 5) = x^2 + 5x+ 2x+ 10 = x^2 + 7x+ 10