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2.3 Exponents and Powers I can read powers and express numbers using exponents Vocabulary Exponent: the small number written above and to the right of a number called the base. It tells how many times to multiply the base by itself. exponent Example: 25 = 2 x 2 x 2 x 2 x 2 = 32 base 2 multiplied by itself five times 25 is read “two to the fifth power” Powers: numbers expressed using exponents Squared: a number multiplied by itself two times; a number to the power of two. Example: 4 squared is 42 = 4 x 4 = 16 Cubed: A number multiplied by itself three times; a number to the power of three. Example: 4 cubed is 43 = 4 x 4 x 4 = 64 Value: How much the expression is worth once multiplied out Notes: 10 is a special case. 10 raised to any power is simply the number 1 with the same number of zeros as the exponent. Examples: 103 = 1 with 3 zeros = 1,000 108 = 1 with 8 zeros = 100,000,000 Applications 1) Write the product using exponents: a. 3 x 3 x 3 x 3 x 3 = ____________ b. 20 x 20 x 20 x 20 x 20 x 20 x 20 x 20 = ___________ 2) Write each power as the product of the same factor. Then find the value. a. 73 = ______ = 7 x 7 x 7 = 49 x 7 = 343 b. 105 = __________________________________ 3) Write the prime factorization using exponents: a. 36 36 6 3 2 b. 96 6 3 2 36 = 2 x 2 x 3 x 3 = 22 x 32 2.3 Exponents and Powers