Chapter 7 Flashcards
Exponents and Exponential Functions
What is a Monomial?
A momonial is a number, a variable, or the product of a number and one or more variables with nonnegative integer exponents
What to monomials not contain?
- Addition or subtraction
- Variables in the denominator
- Negative exponents
Monomial? -x+5
No: Contains addition
Monomial? 23abcd^2
Yes
What is y.y.y.y?
y^4
What is 3.y.x.3.y.x.?
9 x^2 y^3
Combining like terms
Add coefficients
Do not alter exponents
Multiplying monomials
Multiply coefficients
Add exponents
What is ^3(m^6)?
m^9
What is (-4rx^2t^3)(-6r^5x^2t)?
24r^6x^4t^4
Power of a Power
(a^m)^p=a^mp
Product of Powers
a^m . a^p= a^m+p
Power of a Product
(ab)^m=a^mb^m
What is -6^2?
-36
What is (-6)^2?
36
What is (n^3)^6?
n^18
What is (4x)^2?
16x^2
What is (3xy^4)^2(-2y)^6
576x^2y^14
Quotient of Powers
a^m/a^p=a^m-p
Power of a Quotient
(a/b)^m=a^m/b^m
Zero Exponent Property
a^0=1
Negative Exponent Property
a^-n=1/a^n
Exponent IS present in the ()
- Multiply Exponents
- Raise coefficient to power
No exponent outside the ()
- Simplify the coefficients
- Move variables to make positive
- Large exponent - small exponent
- Put where the large exponent was
- Add exponents
What is x^3y^4/x^2y?
xy^3
What is (12x^6y^8/2x^5y^99)^0?
1: Anything to the power of zero
Exponent outside the parenthesis
- Simplify the inner fraction
- Raise the numerator to the power
- Raise the denominator to the power
[` Symbolizes a radical
OK OK OK OK
Rational Number
A number that can be expressed as a fraction
Rational Exponents
Are exponents expressed as fractions
Square Root
b^1/2=b`7
Cube Root
b^1/3=3[`b
nth Root
b^1/n=n[`b
Complex Roots
b^m/n=(n[`b)^m
What is 19^1/3?
3[`19
What is [`38?
38^1/2
3[`64 on calculator
3 2nd ^ 6 4 =
Power Property of Equality
If 5^x=5^3 then x=3
What is 6^x=1296?
6^x=6^4
x=4
STUDY 7.5 ON PAPER
EXPONENTIAL FUNCTIONS
