Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 2: Exponents - Coggle Diagram
Chapter 2: Exponents
consists of
Higher Exponents
consists of
cube
which is the number
raised to power 3
perfect cube
which is the cube of
an integer
means
power of a^n
consists of
Power of Quotient [ (a / b)^n = a^n / b^n]
Power of Negation
n (even): [ (-a)^n = a^n ]
n (odd): [ (-a)^n = -a^n ]
Cube of Negation [ (-a)^3 = -a^3 ]
Product of powers (same base) [ a^n . a^m = a^(n+m) ]
Quotient of powers (same ase) [ a^n / a^m = a^(n-m) ]
Power of Reciprocals [ (1/a)^n = 1/a^n ]
Power of power [ (a^n)^m = a^(nm) ]
Power of Product [ (ab)^n = a^n b^n ]
Power 1 [ a^1 = a ]
Zero as an exponent
means
a^0 = 1
Squares
is the product of
number with itself
written with
the power 2
for integers are
perfect squares
consists of
square of reciprocals
squares of quotient
square of a sum
squares of negation
squares of product
Negative Exponents
when n is positive
a^(-n) is the reciprocal of a^n [ a^(-n) = 1 / a^n ]
consists of
Product of powers (same base) [ a^n . a^m = a^(n+m) ]
Power of Reciprocal [ (1/a)^(-n) = a^n ]
Exponents
known as
power
consists of
base
exponent
used in the process
exponentiation
follows the
exponent laws