Understanding Exponents and Powers: Basics and Evaluations
This guide introduces the concept of exponents and powers, explaining expressions like (2^3) (two to the third power or two cubed) and (3^2) (three to the second power or three squared). It covers how to identify the base and exponent, along with the use of variables raised to powers, such as (x^6). The section also emphasizes the importance of grouping symbols, like parentheses and brackets, in expressions, demonstrating their impact on calculations. Learn how to evaluate powers with examples and explore how input values affect results differently based on grouping.
Understanding Exponents and Powers: Basics and Evaluations
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Presentation Transcript
Exponents and Powers • An expression like 23 is called a power • 23 = 2 2 2 = 8 • This expression is read as “two to the third power” or “two cubed” • The repeated factor is the base • The exponent indicates how many times the base is used as a factor • A power with an exponent of 2 such as 32 can be read as “three to the second power” or “three squared” • Variables can also be raised to a power • For example, x6 is x to the sixth power, or x ∙x ∙x ∙x ∙x ∙x • Evaluate a power by replacing the variable with its value and calculating the answer • Evaluate x4 for x = 3 • Evaluate x4 for x = -3 • Did you get the same answer? Why or why not? base →23 ←exponent
Grouping symbols • Grouping symbols enclose parts of an expression that represent a single number • Parentheses ( ) • Brackets [ ] • Braces { } • Absolute value symbols | | also act as grouping symbols • A fraction bar is another grouping symbol • The numerator and denominator are separate expressions • Grouping symbols affect the result of power expressions • For example • -22 = -4, while (-2)2 = 4 • 1 + 23 = 9, while (1 + 2)3 = 27
