CHARTS & TABLES Properties and Theorems
CHARTS & TABLES Properties and Theorems
Properties and Theorems (continued)
Power of a Quotient Property
If b≠ 0
(a/b)m=am/bm
Powers Property of Equality
If a=b
then an=bn.
Product of Powers Property
am×an=am+n
Property of Exponentials
If ax=ay, then x=y
and
If ax=bx, then a=b
Pythagorean theorem
a^2 +b^2 =c^2
and
c^2 =a^2 +b^2
Quadratic Formula
ax^2 +bx+c= 0
Quotient of Power Property
If a≠ 0
am/an=am–n
Rational Exponent Theorem
If x> 0
xm/n= (x1/n)m
and
xm/n= (xm)1/n
Reflexive Property of Equality
a=a
Root of a Power Theorem
If x> 0, and n≥2, and mand nare integers
n√–xm= (n√–x)m=xm/n
Root of a Product Theorem
If n> 1, and xand yare positive real numbers
n√–xy=n√–x·n√–y(continues)