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Power Laws

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Andrew Grichting
Andrew Grichting

This document discusses various methods for estimating and calculating square roots. It begins by defining irrational numbers as non-repeating decimals that can result from taking the square root of a non-perfect square. It then discusses estimating square roots by knowing perfect square numbers and using guess and check methods. Later sections cover using calculators, applying square roots in formulas, exponent rules including multiplication, division, powers, and scientific notation for writing extremely large numbers.

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Estimating and Calculating Square Roots 1.1
Irrational Numbers ,[object Object],[object Object],[object Object]
Estimating Square Roots ,[object Object],[object Object]
Estimating Square Roots cont’d ,[object Object]
Estimating Square Roots cont’d ,[object Object]
Estimating Square Roots cont’d ,[object Object]
Estimating Square Roots cont’d ,[object Object],Starting from the decimal, split the number into pairs of digits. Estimate the square root of the group furthest from the decimal. Write one zero for all of the other groups.
Calculators ,[object Object],[object Object]
Multiples of Roots ,[object Object]
Evaluating Square Roots ,[object Object],[object Object]
Applying Square Roots 1.2
Squares ,[object Object],[object Object],345m 2 18.6m
Square Roots in Formulas ,[object Object],[object Object],[object Object],8cm 7cm 5cm
Exponents and Powers 1.4
Definitions ,[object Object],[object Object],[object Object],[object Object],base exponent
Evaluating Exponents ,[object Object],[object Object],[object Object],Exponential form Repeated multiplication form Standard form
Exponents of Variables ,[object Object]
What’s the Base? ,[object Object],-4 2 2 6 a 4 xy 2 x 3 Base Exponent Expression
Coefficient ,[object Object],coefficient -4 3 Coefficient Expression
Exponent Rules 1.5
Multiplication Law ,[object Object]
Multiplication Law cont’d ,[object Object]
Division Law ,[object Object]
Division Law ,[object Object]
Power to a Power Rule ,[object Object]
Power to a Power Rule cont’d ,[object Object]
Scientific Notation Large Numbers 1.7
Extremely Large Numbers ,[object Object],[object Object],[object Object]
Extremely Large Numbers cont’d ,[object Object],[object Object],[object Object]
Scientific Notation ,[object Object],[object Object],[object Object],[object Object]
Scientific Notation cont’d ,[object Object]
Operations With Scientific Notation ,[object Object],[object Object],[object Object]
Operations With Scientific Notation cont’d ,[object Object],[object Object],[object Object]
Operations With Scientific Notation cont’d ,[object Object]
Working With Exponents 1.8
What’s the Difference? ,[object Object]
What’s the Difference? cont’d ,[object Object],-81 81 Value Repeated Mult Expression
Powers of Monomials 1.9
Monomials ,[object Object],These are monomials These are NOT monomials
Power Rule ,[object Object]
Powers of Monomials ,[object Object]
Powers of Monomials cont’d ,[object Object]
Powers of Monomials cont’d ,[object Object]
Powers of Rational Monomials ,[object Object],[object Object]
Products of Monomial Powers ,[object Object],[object Object]
Products of Monomial Powers ,[object Object],[object Object]
Products of Monomial Powers ,[object Object]
Volumes ,[object Object],s
Volumes ,[object Object],[object Object],Hint:
Zero and Negative Exponents 1.11
Zero Exponents ,[object Object],[object Object]
Zero Exponents ,[object Object],[object Object]
Zero Power ,[object Object]
Negative Powers ,[object Object],[object Object]
Negative Powers ,[object Object],[object Object]
Negative Exponents ,[object Object],[object Object]
Negative Exponents ,[object Object],[object Object]
Negative Exponents ,[object Object]
Scientific Notation Small Numbers 1.12
Very Small Numbers ,[object Object],[object Object],The pH of neutral water is 7.
Small Numbers ,[object Object],[object Object],The pH of sodium hydroxide solution is 14.
Operations With Scientific Notation ,[object Object],[object Object],[object Object]
Operations With Scientific Notation ,[object Object]

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