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Write the product as a simplified power
(-8)4(-8)8
(-8)12
Find the Square Root. State NR if no real root exists...
16
4
What is GEMDAS, what does each section include, and how do we apply it?
GEMDAS is the Order we do Operations on mathematical equations, first to last, then from left to right.
G- Grouping Symbols are () [] || fraction bars, radical signs
E- Exponents
MD- Multiplication & Division (whichever is first left to right)
AS- Addition & Subtraction (whichever is first left to right)
In Addition this Property looks like this...
a + b = b + a
In Multiplication this Property looks like this...
ab = ba
Commutative
Is a set Closed or Not Closed if positive integers are under multiplication?
Closed
A positive integer times a positive integer always produces a positive integer (In the set)
Ex: 5 x 5 = 25
Simplify the Expression
77/74
73
Write & Solve the Square Root. State NR if no real root exists...
Square Root of 144
Write \/‾‾144
Solve 12
Name the order you should complete Operations and give your solution in this simple equation...
2 x 42 x (1 + 3)
Addition (1 + 3) = 4
Exponents 42 = 16
Multiplication & Division left to right 2 x 16 x 4
Solution 128
In Addition this Property looks like this...
(a + b) + c = a + (b + c)
In Multiplication this Property looks like this...
(ab)c = a(bc)
Associative
Is a set Closed or Not Closed when negative integers are under multiplication?
Not Closed
A negative number x A negative number produces a positive integer (Not in the Negative set)
Ex: -5(-5) = 25
84 * 86 / 85
85
Write & Solve the Root Equation. State NR if no real root exists...
Cube Root of -125
Write 3\/-1̅2̅5̅
= -5
Remember this rule: Cube roots are odd so Negatives Allowed
Evaluate the Expression
|4 - 22| + (62 - 6)
30
In Addition this Property looks like this...
a + 0 = 0 + a = 0
In Multiplication this Property looks like this...
a x 1 = 1 x a = a
Identity
Name this Property under Addition
(10x + 5) + 7x = 7x + (10x + 5)
Commutative Property
Remember the property Commutes... You can move it!
Evaluate the Equation
1830
1
Remember this: Any number to the power of 0 is divided by itself... meaning it is always 1
Evaluate this root expression, state if there is no real root.
\/‾‾-49
No Real Root
Remember This Rule:
Square Roots of negative numbers are ALWAYS NOT REAL. If there is a negative symbol outside this condition doesn't change -\/‾‾-49.... \/‾‾-144... -\/‾‾-25... still NOT REAL, NEVER REAL
Evaluate the Expression
(3x2)3
27x6
These Properties are unique...
In Addition this Property looks like this...
a + (-a) = -a + a = 0
In Multiplication this Property looks like this...
a s 0 = 0 x a = 0
Additive Inverse Property
&
Zero Property of Multiplication
Find the consecutive integers \/‾‾47 lies between
Answer: 6 and 7
Step 1 Identify perfect squares around 47:
36 < 47 < 49
Step 2 take the square roots to find the integers:
\/‾‾36 = 6 & \/‾‾49 = 7
Step 3 Conclude
\/‾‾47 falls between 6 and 7
Evaluate the Exponential Expression
(5 / h2)3
53/h2(3) = 125/h6
Write & Evaluate this root expression, state if there is no real root.
Plus minus the square root of 36
± \/‾‾36 = ±6
Evaluate the Expression...
(3-1x4y-5)5
--> 3-1(5)x4(5)y-5(5) --> 3-5x20y-25
= x20 / 35 y25
I'm a property that works with addition, subtraction, and multiplication but not division..
example: for any integers a and b, ab is an integer...
Closure of Integers
Is this Expression Positive or Negative?
|-4|3(-29)-4 / (21 - 25)2
Determine if the elements are positive or negative and make your deduction:
(positive)(positive) / (positive)
Rule to Remember
If the number of negative elements is odd --> the final answer is negative
If the number of negatives is even --> the final answer is positive