Lesson 2 - Lesson 2 Exponential Notation: Where is the base...

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Unformatted text preview: Lesson 2 Exponential Notation: Where is the base and is the exponent or power Product Rule for Exponents: When common bases are multiplied, the exponents are added Quotient Rule for Exponents: When common bases are divided, the exponents are subtracted (exponent in numerator minus exponent in denominator) Power Rule for Exponents: () When a base is raised to a power and then raised to another power, the exponents are multiplied Product to a Power Rule: ( ) ( ) When a product is raised to a power, the exponent is distributed to each factor Quotient to a Power Rule: ( ) ( ) When a quotient is raised to a power, the exponent is distributed to each factor in the numerator and denominator Zero-Exponent Rule: ( ) Any base taken to the power of zero is 1, except a base of zero; Negative Exponent Rule: ( ) ( ) To change the sign of an exponent, take the reciprocal of the base; if a quantity has a negative exponent, take the reciprocal of the entire quantity; keep in mind that the sign of the base DOES NOT change Radical Notation: Where is the radicand, radical sign √ is the index or root and √ is the Definition of √ - the value that must be multiplied by itself produce (√ √ ) ( (√ √ √ times to ) (√ ) ) Think of this as undoing exponential notation If the index is even, the radicand nonnegative. Why? If the index is odd, the radicand positive, negative or zero. Why? and the radical √ must be and the radical √ can be Example 1: Evaluate each expression a. √ b. √ c. √ d. √ e. √ Using the definition, if , then in for , we have the following: √ √ √ || Why? Example 2: Evaluate each expression ) a. √( b. (√ c. √( ) ) d. √ e. √( ) √ ; if we substitute In part b. of the previous example, we saw that (√ ((√ ) ) ). Given that this is true, what is √ exponential notation? In other words, √ ( in . ) Why? Go back and re-work part b. from the previous example. (√ Definition of equivalent to √ exists ) – the radical expressions √ , where and ( √ ) are is a positive integer greater than and Example 3: Convert the following expressions to radicals and simplify a. b. c. d. e. ( ) The laws of exponents are true for rational (fractional) exponents Example 4: Rewrite the radicals using rational exponents, then use exponent rules to separate the radicands a. √ b. √ Product Rule for Radicals: - when indices are the same, radicands can be multiplied (only works if roots exist); when indices are not the same, use rational exponents; Simplifying radicals: - remove factors from the radical until no factor in the radicand has a degree greater than or equal to the index Example 5: Simplify a. √ b. √ √ Rationalizing denominators: - The process by which a fraction is rewritten so that the denominator contains only rational numbers Example 6: Rationalized the denominator a. √ b. √ c. √ ...
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This document was uploaded on 01/23/2012.

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