To raise a power to a power. multiply the exponents. ex. (2+2)4= 44= 256 power rule can be applied to both products and quotients
Author: Judy - Ling Hing
1.6: Exponent Laws
If the exponent have the same base all raised to the same power, it will equal ‘1’ Anything to the power of 0 will always equal ‘1’ when there is an exponent multiplying another exponent with the same base, add the exponents to simplify it when there is an exponent dividing another exponent with the…
1.5: Orders of Operations
B Brackets E Exponents D Division M Multiplication A Addition S Subtraction Brackets are the top priority for order of operations. If there are bigger brackets around another set of brackets, work from inside out Exponents are below brackets. If there are no brackets, do exponents first, and if there are brackets, do the brackets…
1.4: Defining a Power
Exponential Notation: ex. 2x2x2x2x2 = 25 ex. 2x2x2x2x2x2= 26 ex. 2x2x2x2x2x2x2= 27 Notes: Even number of negative signs= positive number Odd number of negative signs= negative number –26 is ONLY putting the ‘2’ to the power of 5, NOT the negative. Therefore, the answer would still be negative because (-)(2)(2)(2)(2)(2)(2) = -64 (-2)6 is putting…
1.3: Square Roots of Non-Perfect Squares
Non Perfect Squares: numbers that can’t be multiplied into by two of the same rational numbers Ex. √48, √33, √6 These numbers are non-perfect squares because no numbers can multiply into it by itself (2×2 won’t work, 3×3 won’t work, 4×4 won’t work, 5×5 work work etc.) non-perfect squares are considered to be irrational
1.1: The Real Number System
Natural Numbers: Positive Whole Numbers (no decimals or fractions) NOT INCLUDING ‘0’ ex. 1,2,3,4,5,6,7,8,9,10,11……….. Whole Numbers: Positive Whole Numbers (no decimals or fractions) INCLUDING ‘0’ ex. 0,1,2,3,4,5,6,7,8,9,10,11……….. Integers: All Whole Numbers (no decimals or fractions) that are positive or negative. ex. -5,-4,-3,-2,-1,0,1,2,3,4,5 Rational Numbers: Any numbers that can be turned into a fractions. ex. 2,…
2.1: Polynomials
Polynomial: An expression that contains variables and coefficients ex. 5xy2 – 3x + 5y3 – 3 Term: A term consists of a variable and a coefficient ex. 5x Monomial: A polynomial containing only ‘1’ term ex. 5xy2 Binomial: A polynomial containing ‘2’ terms ex. 5xy2 – 3x Trinomial: A polynomial containing ‘3’ terms ex. 5xy2 – 3x + 5y3 …
4.2: Linear relations
Linear relation: A relationship between the independent and dependent variable. Represented as a straight line on a graph. Rate of Change: A rate that describes how one quantity changes in relation to the other quantity Variable: A letter that represents a quantity that can change Operations: addition , subtraction, multiplication, division, exponents Expression: A mathematical…
3.1 Rational Numbers
Rational Numbers: Any numbers that can be expressed as a quotient or fraction Irrational Numbers: Any numbers that CAN’T be expressed as a fraction (Numbers that are not rational.) Notes: ALL integers are rational, ALL fractions are rational, ALL terminating decimals are rational, ALL repeating decimals are rational Examples of Rational Numbers: 5, -5, 1/2,…
1.2: Square Roots
Perfect Square: A number with a rational square root. Exponents: The exponent is the smaller number on top of the bigger number, tells you how many times to multiple the base number by itself. Eg. 54. In this case, the ‘4’ is the exponent. Base: The Base is the bigger number. It is what you…