32 terms

Radical Exponents

^n√a=^1/n

Negative even powdered roots

No real roots (i.e. √-4 = no real roots)

Negative odd power roots

-2 (i.e. ^3√-8 = -2)

Exponent radical

(-27)^2/3 = (^3√27)^2

Canceling exponents

(g+10)^5(1/5) = 70^1/5

Multiplication rule

a^m • a^n = a^m+n

5^1/2 • 5^3/2 = 5^4/2 = 5^2 = 25

5^1/2 • 5^3/2 = 5^4/2 = 5^2 = 25

Power to a power

(a^m)^n = a^m•n

(3^5/2)^2 = 3^5 = 243

(3^5/2)^2 = 3^5 = 243

Product to a power

(ab)^m = a^m•b^m

(16•9)^1/2 = 16^1/2 • 9^1/2 = 4•3 = 12

(16•9)^1/2 = 16^1/2 • 9^1/2 = 4•3 = 12

Negative exponents

a^-m = 1/a^m

36^-1/6 = 1/36^1/2 = 1/6

36^-1/6 = 1/36^1/2 = 1/6

Quotient rule

a^m/a^n = a^m-n

4^5/2/4^1/2 = 4^4/2 = 4^2 = 16

4^5/2/4^1/2 = 4^4/2 = 4^2 = 16

Quotient to a power

(a/b)^m = a^m/b^m

(27/64)^1/3 = 27^1/3/64^1/3 = 3/4

(27/64)^1/3 = 27^1/3/64^1/3 = 3/4

Combine like terms

ax^+/-bx^m = (a+/-b)x^m

2y^1/2 - 5 ^1/2 = -3y^1/2

2y^1/2 - 5 ^1/2 = -3y^1/2

Operations on functions (+)

h(x) = f(x) + g(x)

Operations on functions (-)

h(x) = f(x) - g(x)

Operations on functions (x)

h(x) = f(x) x g(x)

Operations on functions (/)

h(x) = f(x)/g(x)

composition of a function

g(f(x))/f(g(x))

inverse

x = y, y = x

(1,2) (2,1)

(1,2) (2,1)

inverse relation

a reflection of the original relation across the line y = x

inverse functions

when both the original relation and the inverse are functions

f^-1(x)

f^-1(x)

horizontal line test

the inverse of a function f is also a function if and only if no horizontal line intersects the graph of f more than once

vertical line test

the inverse of a function f is also a function if and only if no vertical line intersects the graph of f more than once

square root table

0,0 1,1 4,2

cubed root table

-1,-1 o,o 1,1

a

vertical stretch

h

translates the graph h units horizontally (x- axis) (vertical form)

k

translates the graph k units vertically (y-axis) (vertical form)

extraneous solutions

an apparent solution that must be rejected because it does not satisfy the original equation

Canceling squared roots

√x = (√x)^2

Cancel cubed root

^3√x = (^3√x)^3

Solving radical equations

GEMDAS

Solving radical equations (reminder)

factored solutions = 2 answers = cancel one of them so the original equation makes sense