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Positive and Negative Exponents

Positive and Negative Exponents. Module VI, Lesson 1 Online Algebra VHS@pwcs. What is an exponent?. An exponent is a shortcut for writing repeated multiplication. 5 4 5 is a base 4 is the exponent, it tells us how many times we multiply the base by itself. = 5 * 5 * 5 * 5. = 625.

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Positive and Negative Exponents

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  1. Positive and Negative Exponents Module VI, Lesson 1 Online Algebra VHS@pwcs

  2. What is an exponent? • An exponent is a shortcut for writing repeated multiplication. 54 5 is a base 4 is the exponent, it tells us how many times we multiply the base by itself. = 5 * 5 * 5 * 5 = 625

  3. 43 26 34 22 * 53 Click to get the answers. 4 * 4 * 4 = 64 2 * 2 * 2 * 2 * 2 * 2 = 64 3 * 3 * 3 * 3 = 81 2 * 2 * 5 * 5 * 5 = 500 Simplify the following:

  4. Do you see any patterns? • Did you notice that when we subtract 1 from the exponent we take away a zero? • What happens when our exponent becomes negative? • Another way to think about taking away a zero is to move the decimal point one place to the left.

  5. Another pattern? • What is the fraction equivalency to each decimal? • Notice that: • 10-1 = 1/10 = 1/101 • 10-2 = 1/100 = 1/102 • 10-3 = 1/1000 = 1/103 • 10-4 = 1/10000 = 1/104

  6. Zero as an Exponents The first property of exponents is: • In algebra: a0 = 1 • In English: any number to the zero power is 1! Try these! • 450 • x0 • 2r0 • The r is the only thing taken to the 0 power. • So the answer is 2(1) or 2. = 1 = 1 = 2

  7. Negative Exponents The next property of exponents is: • a-x = or = ax • I like to look at negative exponents this way: • First recall that x = , so I think of all numbers/expressions as fractions. • the negative exponent is in the numerator, then I switch the number/variable to the denominator. • If the negative exponent is in the denominator, then I switch the number/variable to the numerator.

  8. Simplify the following: • c-5 • We switch the c-5 to the bottom of the fraction, and make it positive. • We need something in the numerator, so it is 1, making our answer:

  9. Simplify the following • We switch the d-4, to the top of the fraction, leaving a 1 in it’s place: • If we simplify we get: d4.

  10. x-3y5 The only variable with a negative exponent is the x, so that is the only exponent we move. Now the things taken to a negative exponent are the a and the b, so these are what we move. Simplify these:

  11. Exponent Recap! • An exponent is a short cut to writing repeated multiplication. It tells us how many times we multiply a base by itself. • Any number to the zero power is 1 • When dealing with negative exponents, think of all numbers/expressions as fractions. • Then switch all variables taken to negative exponent to the opposite side of the fraction bar, making the exponent positive.

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