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# Ch4 Fac, Frac, Exp

### Study for test

Rules for divisibility 2: Ends with an even # (0,2,4,6,8) 3: Sum of the digits are divisible by 3 (2+4+6=12) is divisible by 3 4: The last two #'s are divisible by 4 (2/48) 4 and 8 are divisible by 4 5: Ends in a 5 or 0 6: Divisible by 2&3 8: The last 3 #'s are divisible
Rules for divisibility 9: Sum of digits are divisible by 9 10: Ends in 0
Order of operations The mathematical rules that determine the correct order for solving any sequence of math operations. Powers and roots are solved before multiplication and division, which in turn are solved before addition and subtraction.
Exponent An Exponent is a mathematical notation that implies the number of times a number is to be multiplied by itself. Example: In 24, 4 is the exponent. It indicates that 2 is to be multiplied by itself 4 times. 24 = 2 × 2 × 2 × 2 = 16
Base In an expression of the form xy, x is the base. The base x is a factor that repeats y times. Example: In 34, 3 is the base. The factor 3 would repeat 4 times, i.e. 3 × 3 × 3 × 3
Power Power or Exponent tells how many times a number is multiplied by itself. Example: In 35, 5 is the power or exponent and 3 is the base
(-3)² means Means that it is negative
-3² means Means the opposite of negative so it is positive
Prime Numbers A prime number that has exactly two factors, 1 and the number itself. Example: 2, 3, 5, 7, 11, 13, 17, 19, etc. are all prime numbers. There are infinitely many prime numbers.
Composite Numbers A whole number that has factors other than 1 and the number itself is a Composite Number. Example: 4, 6, 9, 15, 32, 45
GCF Greatest common factor is the greatest number that is a factor of each of two or more given numbers. Example: the GFC of 24 and 15 is 3
Variable GCF Variables are (usually) letters or other symbols that represent unknown numbers or values. Example: 2x + 5 = 10, x is the variable
Example: X² Y⁵ XY³ X³ Y⁸
Prime Factorization Prime factorization is to write a composite number as a product of its prime factors. Example: 48 is 2 × 2 × 2 × 2 × 3 = 24 × 3.
Example: 120 2*2*2*3*5=24 x 5
Finding Prime factorization using GCF You have to find factors that appear in both factorizations and multiply them together to get the greatest common factor. Use factor trees.
Example: 78 and 124 2
Simplifying variable expressions Like terms are those terms which contain the same powers of same variables. They can have different coefficients, but that is the only difference
12x³ y⁵/8x⁴ y² 96 x¹² y¹⁰
Rational Numbers Any number that can be written in the form A/B where B doesn't equal 0 any number that can be written into a fraction
Give examples of rational numbers 3/5, 10.3 ,0.6, 12/5, 3/5
Negative Rational Numbers if the denominator and numerator are negative they turn positive and only the top number can be negative
How do you write ???????
Multiplying exponent rule Multiplying powers write the same base
4x³y⁵Times 3x² yz² 12 x⁶ y¹⁰
Power of power rule multiplying powers with the same base by multiplying the exponents to the power, combine exponents together, ( aᴹ) ᴺ = a ᴹ*ᴺ (x⁴)⁶ = x ⁴*⁶ = x²⁴
( x³ y⁵)⁴ x¹² y²⁰
Zero exponent rule Any number written to the zero power - the answer is one
x⁰ = 1
Negative exponent rule Rewrite as its reciprocal with a positive power
x⁻³ 1/x³
Write without negative exponents you move the numbers that are negative, to the opposite side that they were on and if they are positive they stay where they are,
x⁻³y²/a²b³ y² / x³ a² b³
rewrite without zero or negative exponents and simplify you take the negative numbers and move them up to the top of the fraction bar and they become positive then add variable together
x⁻³y²z⁰/x⁻²y⁻³ x² y² y² z⁰/ x³= y⁴ /x¹