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4.1 Exponents

This educational resource focuses on the concept of exponents, including how to write and simplify expressions involving them. Exponents indicate repeated multiplication, illustrated through various examples and practices, such as simplifying products of numbers and writing numbers in exponential form. The lesson also includes evaluation of expressions where variables are substituted with specific values. Engaging facts about exponents and a set of homework and challenge problems are provided to reinforce learning.

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4.1 Exponents

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  1. 4.1 Exponents • Objective: To write and simplify expressions involving exponents. • Warm – up: Simplify:1) 3∙3 2) (-1)(-1) 3) 2∙2∙24) (-2)(-2)(-2)(-2)(-2)5) 4∙4∙4

  2. 4.1 Exponents Introduction of Exponents In this notation: 4 is the base 5 is the exponent How are each determined? • The number 16 can be written as 4∙4 and is called a power of 4. • 41 = 4 (“four to the first power”) • 42= 4∙4 (“four to the secondpower”) • 43= 4∙4∙4 (“four to the third power”) • 44= 4∙4∙4∙4 (“four to the fourthpower”)

  3. 4.1 Exponents Write the following in exponential form: 64 a6 -6p6q6 • 6∙6∙6∙6 • a∙a∙a∙a∙a∙a • -2∙p∙q∙3∙p∙q∙p

  4. 4.1 Exponents Write the following in exponential form: Evaluate: x2 if x = -5 x3if x = -5 x4 if x = -5 x5if x = -5 • (2y)3 • 2y3

  5. 4.1 Exponents Simplify: Evaluate: (2a + b)2 if a = 3 and b = -2 if x = 2 and y = 5 • (1 + 5)2 • 1 + 52

  6. 4.1 Exponents Fun Facts!! • Exponents help with area and volume! 2xx A = • 10100, which is 1 with 100 zeros after it, is called a googol!! • Homework: • Pg. 143 Written Exercises#4 – 18 even, 20 – 22,24 – 30 even • Challenge Problems:#32 – 48 even

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