Lesson: Exponents Quick Guide

There are four operations you have to be able to do There are four operations you have to be able to do with exponents There are four operations you have to be able to do with exponents Addition/Subtraction There are four operations you have to be able to do with exponents Multiplication/Division Addition/Subtraction There are four operations you have to be able to do with exponents Exponents to Exponents Multiplication/Division Addition/Subtraction There are four operations you have to be able to do with exponents Exponents to Exponents Negative exponents Multiplication/Division Addition/Subtraction First, addition and subtraction First, addition and subtraction To add or subtract terms, they must be First, addition and subtraction To add or subtract terms, they must be 'like terms' Like terms have to have the same letter First, addition and subtraction To add or subtract terms, they must be 'like terms' Like terms have to have the same letter First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' Like terms have to have the same letter First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same letter Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents 2x ^{2}then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents 2x ^{2} +then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents 2x ^{2} + 3x^{2}then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents 2x ^{2} + 3x^{2} =then they can be added or subtracted Like terms have to have the same letter and those letter have to have the same exponents First, addition and subtraction To add or subtract terms, they must be 2x ^{2} 3x^{2}'like terms' same exponents 2x ^{2} + 3x^{2} = 5x^{2}Notice that when we add/subtract like terms Notice that when we add/subtract like terms the exponent doesn't change Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2}Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2} +Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2} + 3x^{2}Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2} + 3x^{2} =Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2} + 3x^{2} = 7x^{2}Notice that when we add/subtract like terms the exponent doesn't change 4x ^{2} + 3x^{2} = 7x^{2}Same exponents 10x ^{3} + 4x^{3} =x -5x ^{4} + 7x^{4} =x Which of these are like terms? Unlike Terms ? 4x ^{3} , 2x^{5}Like Terms ? 2x ^{2} , 3x^{2}When multiplying terms with the same base When multiplying terms with the same base (x ^{2})When multiplying terms with the same base (x ^{2})(x^{3})When multiplying terms with the same base (x ^{2})(x^{3})same base When multiplying terms with the same base just add the exponents (x ^{2})(x^{3})When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) =When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = xWhen multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = x^{2}When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = x^{2+}When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = x^{2+3}When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = x^{2+3} =When multiplying terms with the same base just add the exponents (x ^{2})(x^{3}) = x^{2+3} = x^{5}When multiplying terms with the same base just add the exponents 2x ^{2}When multiplying terms with the same base just add the exponents 2x ^{2}•When multiplying terms with the same base just add the exponents 2x ^{2}•4x^{3}When multiplying terms with the same base just add the exponents 2x ^{2}•4x^{3} =When multiplying terms with the same base just add the exponents 2x ^{2}•4x^{3} = 8x^{5}5x ^{3} • 4x^{7} =x 3x ^{4} • x =x When dividing variables with exponents When dividing variables with exponents subtract the exponents When dividing variables with exponents subtract the exponents x ^{5}When dividing variables with exponents subtract the exponents x ^{5}When dividing variables with exponents subtract the exponents x ^{3}x ^{5}When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x ^{5}When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x ^{5-}When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x ^{5-3}When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x ^{5-3}= When dividing variables with exponents subtract the exponents x ^{3}x ^{5}= x ^{5-3}= x ^{2}When dividing variables with exponents notice we use top minus bottom subtract the exponents x ^{3}x ^{5}= x ^{5-3}= x ^{2}When dividing variables with exponents notice we use top minus bottom subtract the exponents x ^{3}x ^{5}= top x ^{5-3}= x ^{2}When dividing variables with exponents notice we use top minus bottom subtract the exponents x ^{3}x ^{5}= top bottom x ^{5-3}= x ^{2}When dividing variables with exponents subtract the exponents x ^{5}x ^{3}When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3}When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-}When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-5}When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-5}= When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}Since the exponent is negative When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}Since the exponent is negative When dividing variables with exponents subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}Negative exponent Since the exponent is negative When dividing variables with exponents the x moves to the denominator subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}Since the exponent is negative When dividing variables with exponents the x moves to the denominator subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}1 denominator Since the exponent is negative When dividing variables with exponents the x moves to the denominator and the exponent becomes negative subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}1 Since the exponent is negative When dividing variables with exponents the x moves to the denominator and the exponent becomes positive subtract the exponents x ^{5}x ^{3}= x ^{3-5}= x ^{-2}1 = x ^{2}1 x ^{8}x ^{2}= x 9xy ^{2}6x ^{6}y^{4}= x y Negative exponents always go Negative exponents always go the opposite place Negative exponents always go so if the negative exponent is in the numerator the opposite place Negative exponents always go so if the negative exponent is in the numerator the opposite place x ^{-3}1 Negative exponents always go so if the negative exponent is in the numerator it moves down and becomes positive the opposite place x ^{-3}1 Negative exponents always go so if the negative exponent is in the numerator it moves down and becomes positive the opposite place x ^{-3}1 = 1 x ^{3}Negative exponents always go so if the negative exponent is in the numerator but if the negative is in the denominator it moves down and becomes positive the opposite place x ^{-3}1 = 1 x ^{3}Negative exponents always go so if the negative exponent is in the numerator but if the negative is in the denominator it moves down and becomes positive the opposite place x ^{-3}x ^{-3}1 1 = 1 x ^{3}Negative exponents always go so if the negative exponent is in the numerator but if the negative is in the denominator it moves down and becomes positive the opposite place x ^{-3}x ^{-3}1 1 = = 1 x ^{3}Negative exponents always go so if the negative exponent is in the numerator but if the negative is in the denominator it moves down and becomes positive the opposite place x ^{-3}x ^{-3}1 1 = = x ^{3}1 1 x ^{3}Negative exponents always go so if the negative exponent is in the numerator but if the negative is in the denominator it moves down and becomes positive the opposite place x ^{-3}x ^{-3}1 1 = = x ^{3}1 1 x ^{3}it moves to the numerator Which of these variables move? x, y, z x, b, c a, b, c a, y, z x ^{-2}yz^{2}ab ^{-1}c^{-2}When taking a power to a power When taking a power to a power (x ^{2})^{3}When taking a power to a power the exponents are multiplied (x ^{2})^{3}When taking a power to a power the exponents are multiplied (x ^{2})^{3}= When taking a power to a power the exponents are multiplied (x ^{2})^{3}= x ^{2•3}When taking a power to a power the exponents are multiplied (x ^{2})^{3}= x ^{2•3}= x ^{6}(x ^{4})^{3} =x |

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