1.1.5 Properties of Exponents and Scientific Notation Key Objectives • Write exponential expressions in expanded form. • Simplify expressions involving exponents. • Simplify expressions involving scientific notation. Key Terms
• Scientific notation is a kind of shorthand that can be used to write really large or really small numbers. Numbers expressed in scientific notation are written as the product of a factor and a power of 10. Example 1 Writing Exponential Expressions in Expanded Form An expression of the form a n is an exponential expression where a is the base, n is the exponent, and the quantity a n is called a power. The exponent indicates the number of times that the base is used as a factor. For example, in the exponential expression 5 3 , 5 is the base, 3 is the exponent, and the value of the power is found by multiplying the base 5 by itself 3 times. 5 3 = 5 ⋅ 5 ⋅ 5 = 125 If the base of a power includes more than one factor, then the base is written in parentheses.
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