Law of Exponents.pptx
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The document discusses exponents and bases. It defines a base as the number being raised to a power in an expression like xn, while the exponent n indicates how many times the base is multiplied by itself. It then provides examples of applying rules like the product, power, product to a power, and quotient rules for exponents when multiplying or dividing terms with the same base.
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Exponents
1) Exponents are used to represent repeated multiplication of a number called the base. Positive exponents represent the number of times the base is multiplied, while negative exponents represent the reciprocal of the base raised to a positive power.
2) Scientific notation is a way of writing numbers as a decimal between 1 and 10 multiplied by a power of 10. It allows for easy representation of very large or small numbers. Numbers are converted between scientific and standard notation by moving the decimal point and adjusting the exponent accordingly.
3) Exponents follow specific rules when numbers are multiplied, divided, raised to a power, or involve multiple terms. These rules allow simplification of exponential expressions.
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This document discusses recursion, including:
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- Recursive solutions are generally less efficient than iterative ones but work for some problems.
- Examples include computing powers and factorials recursively, and solving the Towers of Hanoi puzzle recursively by breaking it into smaller subproblems.
Laws of exponents
The document defines exponents and the laws of exponents. It explains that exponents indicate how many times the base is multiplied by itself. The laws covered are: 1) multiplying powers adds the exponents, 2) dividing powers subtracts the exponents, 3) raising a power to a power multiplies the exponents, 4) applying an exponent to a product applies it to each factor, 5) applying an exponent to a quotient applies it to the numerator and denominator, 6) a negative exponent changes the base to its reciprocal with a positive exponent, and 7) any base with an exponent of zero equals one. Examples are provided to illustrate each law.
Exponent 2
The document discusses exponent rules for multiplying, dividing, raising powers, and applying exponents to products and quotients. It provides examples and practice problems for each rule. The key rules are: when multiplying terms with the same base, add the exponents; when dividing terms with the same base, subtract the exponents; when raising a power to another power, multiply the exponents; when applying an exponent to a product or quotient, raise each term in the product or quotient to that exponent.
Rules of exponents 1
The document discusses exponent rules for multiplying, dividing, raising powers, and applying exponents to products and quotients. It provides examples and practice problems for each rule. The key rules are: when multiplying terms with the same base, add the exponents; when dividing terms with the same base, subtract the exponents; when raising a power to another power, multiply the exponents; and when applying an exponent to a product or quotient, raise each term in the product or quotient to that exponent.
Chapter4.3
The document discusses rules for operations involving exponents, including:
- Multiplying powers with the same base by adding the exponents
- Dividing powers with the same base by subtracting the exponents
- Raising a power to a power by multiplying the exponents
Examples are provided to illustrate multiplying, dividing, and raising powers to powers according to these rules. A quiz with problems applying the rules concludes the document.
La potenciación
1. The document provides definitions and examples for exponents and powers. It explains the rules for addition, subtraction, multiplication and division of exponents.
2. Students are assigned problems applying the rules of exponents, including expressing powers with radicals, fractional exponents, and positive exponents.
3. The assignment is due on April 23rd and involves simplifying expressions using the rules of exponents, as well as expressing powers in different but equivalent forms.
Exponents and powers by arjun rastogi
EXPONENTS AND POWERS MUST SEEEEEEEEEEEEEE
IF YOU WANT ME TO MAKE YOUR OWN SUBJECT PPT CALL ME ON NUMBER
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1) Exponents are used to represent repeated multiplication of a number called the base. Positive exponents represent the number of times the base is multiplied, while negative exponents represent the reciprocal of the base raised to a positive power.
2) Scientific notation is a way of writing numbers as a decimal between 1 and 10 multiplied by a power of 10. It allows for easy representation of very large or small numbers. Numbers are converted between scientific and standard notation by moving the decimal point and adjusting the exponent accordingly.
3) Exponents follow specific rules when numbers are multiplied, divided, raised to a power, or involve multiple terms. These rules allow simplification of exponential expressions.
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This document discusses recursion, including:
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- Recursive solutions are generally less efficient than iterative ones but work for some problems.
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The document defines exponents and the laws of exponents. It explains that exponents indicate how many times the base is multiplied by itself. The laws covered are: 1) multiplying powers adds the exponents, 2) dividing powers subtracts the exponents, 3) raising a power to a power multiplies the exponents, 4) applying an exponent to a product applies it to each factor, 5) applying an exponent to a quotient applies it to the numerator and denominator, 6) a negative exponent changes the base to its reciprocal with a positive exponent, and 7) any base with an exponent of zero equals one. Examples are provided to illustrate each law.
Exponent 2
The document discusses exponent rules for multiplying, dividing, raising powers, and applying exponents to products and quotients. It provides examples and practice problems for each rule. The key rules are: when multiplying terms with the same base, add the exponents; when dividing terms with the same base, subtract the exponents; when raising a power to another power, multiply the exponents; when applying an exponent to a product or quotient, raise each term in the product or quotient to that exponent.
Rules of exponents 1
The document discusses exponent rules for multiplying, dividing, raising powers, and applying exponents to products and quotients. It provides examples and practice problems for each rule. The key rules are: when multiplying terms with the same base, add the exponents; when dividing terms with the same base, subtract the exponents; when raising a power to another power, multiply the exponents; and when applying an exponent to a product or quotient, raise each term in the product or quotient to that exponent.
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The document discusses rules for operations involving exponents, including:
- Multiplying powers with the same base by adding the exponents
- Dividing powers with the same base by subtracting the exponents
- Raising a power to a power by multiplying the exponents
Examples are provided to illustrate multiplying, dividing, and raising powers to powers according to these rules. A quiz with problems applying the rules concludes the document.
La potenciación
1. The document provides definitions and examples for exponents and powers. It explains the rules for addition, subtraction, multiplication and division of exponents.
2. Students are assigned problems applying the rules of exponents, including expressing powers with radicals, fractional exponents, and positive exponents.
3. The assignment is due on April 23rd and involves simplifying expressions using the rules of exponents, as well as expressing powers in different but equivalent forms.
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EXPONENTS AND POWERS MUST SEEEEEEEEEEEEEE
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The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base is multiplied by itself using the exponent.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to another power, multiply the exponents.
5) When taking a power of a product, apply the exponent to each factor.
6) When taking a power of a quotient, apply the exponent to the numerator and denominator.
7) A negative exponent changes the base to its reciprocal with a positive exponent.
8) Any base raised to the zero power equals one.
laws_of_exponents_student_use.ppt
The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base is multiplied by itself using the exponent.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to another power, multiply the exponents.
5) When taking a power of a product, apply the exponent to each factor.
6) When taking a power of a quotient, apply the exponent to the numerator and denominator.
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8) Any base raised to the zero power equals one.
laws_of_exponents_student_use.ppt
The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base is multiplied by itself using the exponent.
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3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to another power, multiply the exponents.
5) When taking a power of a product, apply the exponent to each factor.
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The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base is multiplied by itself using the exponent.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to another power, multiply the exponents.
5) When taking a power of a product, apply the exponent to each factor.
6) When taking a power of a quotient, apply the exponent to the numerator and denominator.
7) A negative exponent changes the base to its reciprocal with a positive exponent.
8) Any base raised to the zero power equals one.
laws_of_exponents_student_use.ppt
The document discusses the eight laws of exponents:
1) Exponential form indicates how many times the base is multiplied by itself using the exponent.
2) When multiplying powers with the same base, add the exponents.
3) When dividing powers with the same base, subtract the exponents.
4) When raising a power to another power, multiply the exponents.
5) When taking a power of a product, apply the exponent to each factor.
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- When raising a power to another power, you multiply the exponents
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- When raising a power to another power, you multiply the exponents
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This PowerPoint lesson teaches students about exponents and the three laws of exponents:
1) The product law which states that when multiplying like bases, add the exponents.
2) The quotient law which states that when dividing like bases, subtract the exponents.
3) The power law which states that when raising a monomial to a power, multiply the coefficient and exponents.
Examples are provided to demonstrate applying each law to simplify exponential expressions. An activity is also included for students to practice identifying and applying the correct law.
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This document introduces basic concepts of variables, expressions, and exponents. It provides examples of writing verbal expressions algebraically and vice versa. Key terms introduced include variables, algebraic expressions, factors, products, powers, bases, and exponents. Examples demonstrate writing expressions for word problems, evaluating powers, and finding the number of squares in a multiplication problem written as an exponent. The purpose is to learn the fundamentals of translating between verbal and algebraic representations.
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- Exponential functions have the form y = bx, where b is a positive real number and x is the variable exponent.
- Natural logarithms use e as the base and are written as ln(x). They can be used to solve exponential and logarithmic equations.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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- 3. BASE AND EXPONENT In the expression xⁿ, x is called the base and n is called the exponent. The whole expression is called the nth power of x. base xⁿ exponent
- 4. BASE and EXPONENT • The base of an exponent is a number that is raised to a certain power. • The exponent represents how many times the base number is multiplied.
- 6. Example: Write each product using exponents a. –(9•9•9•9•9•9•9) b. ab • ab • ab • ab • ab c. 2³ • 2² d. 3⁴ • 3³a
- 7. LAW OF EXPONENTS 1.Product Rule 2.Power Rule 3.Product to a Power Rule 4.Quotient Rule 5.Quotient to a Power
- 8. PRODUCT RULE If m and n are natural numbers , then: xm • xn = xm+n
- 9. Example: 1.ab • ab 2.d⁷e⁴ • d⁵e⁶ 3.f² • f⁸g³ 4.3c² • c⁴ 5.-k⁵m⁹ •-k⁵m⁵
- 10. POWER RULE If m and n are natural numbers , then: (xm)n = xmn
- 11. Example: 1. (b³)⁵ 2. (d⁷)⁴ 3. (f²)⁹ 4. (3c²)⁴ 5. (k⁵m⁹)⁵
- 12. PRODUCT TO A POWER RULE For any factors x and y and integer exponent (x•y)m = x m y m
- 13. Example: 1. (b⁷ • b³)⁵ 2. (d⁷ • d⁹)⁴ 3. (f² • f)⁹ 4. (3b³ • bc²)⁴ 5. (2k⁵m⁹ • k²)⁶
- 14. QUOTIENT RULE
- 15. Example:
- 16. QUOTIENT TO A POWER RULE
- 17. Example: