4.1 The Laws of Exponents

šŸ“– Chapter 4 Exponents and the Exponential Function
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1

001. Q1a

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9.1.4 MATH, EXPONENTS, given simple Exponent, evaluate
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2

002. Q1b

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šŸ“š Related Lectures
8 Math, RADICALS, given.square.of.sqrt, simplify
šŸŽ“ 002. square of mixed radical
šŸŽ“ 001. Square of Sqrt
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3

003. Q1c

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Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
4

004. Q1d

Question
Answer
šŸ“š Related Lectures
9.1.4 MATH, EXPONENTS with NUMERICAL BASE, given.power.of.frac{a}{b}, expand.simplify
šŸŽ“ 003. Power of Negative Rational Number
šŸŽ“ 002. Power of Rational Numbers
šŸŽ“ 001. Squaring a Fraction
5

005. Q1e

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
šŸŽ¬ rP4n6IirbZk
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6

006. Q1f

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Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
7

007. Q1g

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
8

008. Q1h

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
9

009. Q1i

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Negative Base, simplify
šŸŽ“ 003. Negative Base and even power
šŸŽ“ 002. Negative of positive base exponent
šŸŽ“ 001. Exponent negative base ex1
10

010. Q2a

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Answer
šŸ“š Related Lectures
9 Math, Exponents, given.One.Base.Product, solve.sum Positive Powers
šŸŽ“ 001. Same Base, simplify by adding
11

011. Q2b

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Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var.Positive.power.only, simplify.add
šŸŽ“ 001. One Var Exponent Expression, Product
šŸŽ“ 003. Product of Negative base, solve
12

012. Q2c

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Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var.Positive.power.only, simplify.add
šŸŽ“ 001. One Var Exponent Expression, Product
šŸŽ“ 003. Product of Negative base, solve
13

013. Q2d

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Answer
šŸ“š Related Lectures
9 Math, Exponents, given Fraction Base, simplify
šŸŽ“ 002. Subtraction of Powers with equal Fraction base
šŸŽ“ 001. Product of Exponents with fraction base
14

014. Q2e

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var.Positive.power.only, simplify.add
šŸŽ“ 001. One Var Exponent Expression, Product
šŸŽ“ 003. Product of Negative base, solve
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15

015. Q2f

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16

016. Q3a

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Answer
šŸ“š Related Lectures
9 Math, Exponents, given Quotient, solve.subtract
šŸŽ“ 002. Subtraction Rule ex2
šŸŽ“ 001. Subtraction Rule of Exponents ex1
17

017. Q3b

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Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
18

018. Q3c

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
19

019. Q3d

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
20

020. Q3e

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
21

021. Q3f

Question
22

022. Q4a

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given One.Var, simplify.add.subtract
šŸŽ“ 001. Simplify with add and subtraction rules
šŸŽ“ 003. Constants and Algebra, simplify with add and subtract rules
šŸŽ“ 002. Exponents, simplify by Add and Subtraction rules
23

023. Q4b

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Answer
šŸ“š Related Lectures
9 Math, Exponents, given.One.Negative.Base.Product, solve.add
šŸŽ“ 001. Simplifying Negative Base Exponent
24

024. Q4c

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given One.Var, simplify.add.subtract
šŸŽ“ 001. Simplify with add and subtraction rules
šŸŽ“ 003. Constants and Algebra, simplify with add and subtract rules
šŸŽ“ 002. Exponents, simplify by Add and Subtraction rules
25

025. Q4d

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.subtract
šŸŽ“ 001. Power then Subtract
26

026. Q4e

Question
Answer
šŸ“š Related Lectures
9 Math, EXPONENTS, Product and Quotient Rules, Sum and Subtraction Rules combined
šŸŽ“ 002. Ambiguous case is done left to right
šŸŽ“ 001. ADD then Subtract
27

027. Q4f

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, given Fraction Base, simplify
šŸŽ“ 002. Subtraction of Powers with equal Fraction base
šŸŽ“ 001. Product of Exponents with fraction base
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28

028. Q5a

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Answer
29

029. Q5b

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šŸ“š Related Lectures
9.1.4.3 MATH, EXPONENTS, given.Power.of,power, eval.mult.mult
šŸŽ“ 001. Simplifying Exponent of Exponent
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30

030. Q5c

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31

031. Q5d

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šŸ“š Related Lectures
9.1.4.3 MATH, EXPONENTS with NUMERICAL BASE, solve.power.sum
šŸŽ“ 001. Exponent Law, Multiply then add
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32

032. Q5e

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.subtract
šŸŽ“ 001. Power then Subtract
33

033. Q5f

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.subtract
šŸŽ“ 001. Power then Subtract
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34

034. Q6a

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var.Positive.power.only, simplify.add
šŸŽ“ 001. One Var Exponent Expression, Product
šŸŽ“ 003. Product of Negative base, solve
35

035. Q6b

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
36

036. Q6c

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Quotient with One Variable Positive Power, simplify
šŸŽ“ 003. Quotient of Exponent with Division symbol
šŸŽ“ 002. Quotient of Exponents where Denominator Power is bigger
šŸŽ“ 001. Quotient of Exponents with Positive Powers ex1
37

037. Q6d

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given One.Var, simplify.add.subtract
šŸŽ“ 001. Simplify with add and subtraction rules
šŸŽ“ 003. Constants and Algebra, simplify with add and subtract rules
šŸŽ“ 002. Exponents, simplify by Add and Subtraction rules
38

038. Q6e

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given One.Var, simplify.add.subtract
šŸŽ“ 001. Simplify with add and subtraction rules
šŸŽ“ 003. Constants and Algebra, simplify with add and subtract rules
šŸŽ“ 002. Exponents, simplify by Add and Subtraction rules
39

039. Q6f

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given One.Var, simplify.add.subtract
šŸŽ“ 001. Simplify with add and subtraction rules
šŸŽ“ 003. Constants and Algebra, simplify with add and subtract rules
šŸŽ“ 002. Exponents, simplify by Add and Subtraction rules
40

040. Q7a

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Answer
41

041. Q7b

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Answer
42

042. Q7c

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.subtract
šŸŽ“ 001. Power then Subtract
43

043. Q7d

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.add
šŸŽ“ 001. Simplify with Power Rule then Product
44

044. Q7e

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.subtract
šŸŽ“ 001. Power then Subtract
45

045. Q7f

Question
Answer
šŸ“š Related Lectures
11.2.1 ALGEBRA OF INTEGER EXPONENTS, given.One.Var, simplify.mult.add
šŸŽ“ 001. Simplify with Power Rule then Product
46

046. Q8a

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Answer
47

047. Q8b

Question
Answer
šŸ“š Related Lectures
9.1.4 MATH, EXPONENTS with NUMERICAL BASE, given.power.of.frac{a}{b}, expand.simplify
šŸŽ“ 003. Power of Negative Rational Number
šŸŽ“ 002. Power of Rational Numbers
šŸŽ“ 001. Squaring a Fraction
48

048. Q8c

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, given.One.Base.Product, solve.sum Positive Powers
šŸŽ“ 001. Same Base, simplify by adding
49

049. Q8d

Question
Answer
šŸ“š Related Lectures
9 Math, EXPONENTS, Product and Quotient Rules, Sum and Subtraction Rules combined
šŸŽ“ 002. Ambiguous case is done left to right
šŸŽ“ 001. ADD then Subtract
50

050. Q9a

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given.Two.Var, simplify.mult
šŸŽ“ 003. Inside or Outside negative first?
šŸŽ“ 002. Power of Quotient two var
šŸŽ“ 001. Power Rule with Two variables
51

051. Q9b

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Answer
52

052. Q9c

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Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Two Variables, solve.subtract
šŸŽ“ 001. Exponent two variable Using Subtraction Rule to simplify
šŸŽ“ 002. Exponent two variable Using Subtraction Rule to simplify
53

053. Q9d

Question
Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given.Two.Var, simplify.mult
šŸŽ“ 003. Inside or Outside negative first?
šŸŽ“ 002. Power of Quotient two var
šŸŽ“ 001. Power Rule with Two variables
54

054. Q10a

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55

055. Q10b

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Answer
šŸ“š Related Lectures
11.2.2 ALGEBRA OF INTEGER EXPONENTS, given Two.Var, simplify.mult.subtract
šŸŽ“ 001. Two variable, simplify with Mult then Subtract
56

056. Q10c

Question
Answer
šŸ“š Related Lectures
9 Math, EXPONENTS, Product and Quotient Rules, Sum and Subtraction Rules combined
šŸŽ“ 002. Ambiguous case is done left to right
šŸŽ“ 001. ADD then Subtract
šŸŽ¬ kVOOVA2KY1k
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57

057. Q10d

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ B2Tz34LEBi8
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58

058. Q11a

Question
šŸ“š Related Lectures
9.1.4 MATH, EXPONENTS, given Equal Power but Different Base, combine
šŸŽ“ 001. Exponent, Different Base but equal Power
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59

059. Q11b

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ 41ZlyuyLRkg
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60

060. Q11c

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
61

061. Q11d

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ STqFOl6r3VI
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62

062. Q12

Question
Answer
šŸ“š Related Lectures
9.1.4.3 MATH, EXPONENTS, given.Power.of,power, eval.mult.mult
šŸŽ“ 001. Simplifying Exponent of Exponent
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63

063. Q13a

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
64

064. Q13b

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
65

065. Q13c

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ gMfDCEOsQ2o
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66

066. Q13d

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
67

067. Q14a

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Answer
68

068. Q14b

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Answer
69

069. Q14c

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Answer
70

070. Q14d

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Answer
71

071. Q15a

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Answer
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
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72

072. Q15b

Question
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
šŸŽ¬ HNpy7nJjHGA
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73

073. Q15c

Question
Answer
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
šŸŽ¬ uCLWpQCdEA4
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74

074. Q15d

Question
Answer
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
šŸŽ¬ yTjiNgyYY7o
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75

075. Q15e

Question
Answer
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
šŸŽ¬ N28EVdl2tyY
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76

076. Q15f

Question
Answer
šŸ“š Related Lectures
11.2.3 Functions, Integer Exponents, given.f^g, simplify
šŸŽ“ 005. Two step to solve
šŸŽ“ 004. Simplifying Two var to the power of var
šŸŽ“ 003. Exponent of Power
šŸŽ“ 002. Subtraction Example
šŸŽ“ 001. One Var example
šŸŽ¬ ZqWhluyP1so
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77

077. Q16a

Question
Answer
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ v6WbdrHZEgk
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78

078. Q16b

Question
šŸ“š Related Lectures
9 Math, Exponents, Product of Not Equal Base, convert to Prime Base and simplify
šŸŽ“ 003. Prime base to simplify ex2
šŸŽ“ 002. Convert to Prime base to simplify
šŸŽ“ 001. Simplifying two different bases exponent
šŸŽ¬ WYM0pojp88Q
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