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Understanding Powers and Exponents: Simplifying Expressions and Order of Operations

This section covers the evaluation and simplification of powers using exponents while adhering to the order of operations. It defines key components such as bases and exponents and provides examples of how to express numbers using powers. Additionally, it includes practice problems for students to apply the concepts. Topics include evaluating powers, writing expressions with exponents, and simplifying powers with given values. Mastery of these concepts is essential for solving more complex mathematical problems.

samuel-strickland
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Understanding Powers and Exponents: Simplifying Expressions and Order of Operations

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  1. Chapter 4 Section 2 I Can . . . Evaluate and Simplify Powers Use Order of Operations with Exponents HW: 4-2 Ws and pg 180 #11 – 27 ODD SHOW WORK

  2. Powers 26 Means 2 • 2 • 2 • 2 • 2 • 2 Whole Expression is called a Power. Base: The number used in multiplication Exponent: The number of repeated multiplications

  3. Power Verbal Expression Value 121 Twelve to the first power 12 62 Six to the second power 6•6 = 36 or six squared (0.2)3 Two-tenths to the third power (.2)(.2)(.2) = 0.008 or two-tenths cubed -74 The opposite of the quantity of (-1)(7•7•7•7) = -2,401 seven to the fourth power (-8)5 Negative eight to the fifth power (-8)(-8)(-8)(-8)(-8) = -32,768

  4. Using an Exponent Write the expression using an exponent. Student Practice Problems (-5)3 1. (-5)(-5)(-5) 1. 6•6•6•6 64 -2a3b 3xy3 2. -2•a•b•a•a 2. 3•x•y•y•y m2n2 3. m•m•n•n 3. 4 • x • y • x • y 4x2y2

  5. Simplifying a Power Using the Power Key Student Practice Problems The ice age ended about 104 years ago. How many years ago was this? 10 = 10•10•10•10 = 10,000 Simplify: 2a2 if a=7. 2•72 = 2•49 = 98 • A microscope can magnify a specimen 103 times. How many times is that? 103 = 10•10•10 = 1,000 • Evaluate –a4b for a = 2 and b = 3. (-1)(2)4(3) = (-1)(16)(3) = (-16)(3) = -48

  6. Order of Operations with Exponents • Grouping Symbols • POWERS • Multiplication or Division Left to Right • Addition or Subtraction Left to Right 15 + (4 + 6)2÷ 5 15 + (10)2÷ 5 15 + 100÷ 5 115 ÷ 5 23

  7. Student Practice Problems 7(w - 3)3 + z For w = 5 and z = 6 7(5 - 3)3 + 6 7(2)3 + 6 7(8) + 6 56 + 6 62 (12 – 3)2÷ (22 – 1) (9)2 ÷ (22 -1) (9)2 ÷ (4 – 1) (9)2 ÷ (3) 81 ÷ 3 27

  8. Closure Write a numerical expression with exponents. Simplify your expression. Hand your expression to a partner to check your work.

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