this lesson‚ make sure that you develop responses to the essential question listed below. How can an expression written in either radical form or rational exponent form‚ be rewritten to fit the other form? The number inside the radical is the numerator and the number outside the radical sign is the denominator in the rational exponent form‚ if thats right then you just do the same thing with the exponent to find the radical form. Or by by recalling the rule Rational Exponents Radical Expressions The
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Laws of Exponents Here are the Laws (explanations follow): Law | Example | x1 = x | 61 = 6 | x0 = 1 | 70 = 1 | x-1 = 1/x | 4-1 = 1/4 | | | xmxn = xm+n | x2x3 = x2+3 = x5 | xm/xn = xm-n | x6/x2 = x6-2 = x4 | (xm)n = xmn | (x2)3 = x2×3 = x6 | (xy)n = xnyn | (xy)3 = x3y3 | (x/y)n = xn/yn | (x/y)2 = x2 / y2 | x-n = 1/xn | x-3 = 1/x3 | And the law about Fractional Exponents: | | | Laws Explained The first three laws above (x1 = x‚ x0 = 1 and x-1 = 1/x) are just part of
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Number Expanded form Exponential form Base and exponent 10000 10 × 10 × 10 × 10 104 base 10‚ exponent 4 base ‚ exponent 5 64 2 × 2 × 2 × 2 × 2 × 2 26 base 2‚ exponent 6 64 (–2) × (–2) × (–2) × (–2) × (–2) × (–2) (–2)6 base –2‚ exponent 6 –32 (–2) × (–2) × (–2) × (–2) × (–2) (–2)5 base –2‚ exponent 5 Example 1: Write the following in exponential form. a. Minus nine to the power of six b. One fourth to the power of five c. Three square to the power of five Solution:
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Laws of Exponents Exponents are also called Powers or Indices The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64 In words: 82 could be called "8 to the second power"‚ "8 to the power 2" or simply "8 squared" . So an Exponent just saves you writing out lots of multiplies! Example: a7 a7 = a × a × a × a × a × a × a = aaaaaaa Notice how I just wrote the letters together to mean multiply? We will do that a lot here. Example: x6 = xxxxxx
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The Laws of exponents Study Guide…page 1 of 3 Base Number: The number that multiplies by itself as many times as the exponent tells it to. Exponent: The small number that tells the base number how many times to multiply by itself. NOTE: numbers and variables without exponents actually have an invisible 1 as their exponent. | | | |Multiplying exponents
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Laws of Exponents Here are the Laws (explanations follow): Law | Example | x1 = x | 61 = 6 | x0 = 1 | 70 = 1 | x-1 = 1/x | 4-1 = 1/4 | | | xmxn = xm+n | x2x3 = x2+3 = x5 | xm/xn = xm-n | x6/x2 = x6-2 = x4 | (xm)n = xmn | (x2)3 = x2×3 = x6 | (xy)n = xnyn | (xy)3 = x3y3 | (x/y)n = xn/yn | (x/y)2 = x2 / y2 | x-n = 1/xn | x-3 = 1/x3 | And the law about Fractional Exponents: | | | Laws Explained The first three laws above (x1 = x‚ x0 = 1 and x-1 = 1/x) are just part
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Mrs. Cappiello Algebra 2/Trig‚ Period 6 1 April 2012 Exponents and Logarithms An exponent is the number representing the power a given number is raised to. Exponential functions are used to either express growth or decay. When a function is raised to a positive exponent‚ it will cause growth. However‚ when a function is raised to a negative exponent‚ it will cause decay. Logarithms work differently than exponents. Logarithms represent what power a base should be raised to in order to produce a
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text. Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide the class with a third expression to simplify that includes rational (fractional) exponents. The two laws of exponents are For any real number a and any rational exponents m and n: 1. In multiplying‚ we can add exponents if the bases are the same. 2. In dividing‚ we can subtract exponents if the bases are the same
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Exponents and Powers Very large numbers and very small numbers are difficult to read‚ understand‚ and compare. To make this easier‚ we use exponents by converting many of the large numbers and small numbers into a shorter form. For example: 10‚000‚000‚000‚000 can be written as (10)13. Here‚ 10 is called the base and 13 is called the exponent. For any non-zero integer a‚ a m 1 ‚ where m is a positive integer. am a–m is called the multiplicative inverse of am and vice-versa.
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Explanation Zero Exponent Property x0 = 1 (x ≠ 0) Any number (except 0) with an exponent of 0 equals 1. Negative Exponent Property x−n = 1 xn (x ≠ 0) Any number raised to a negative power is equivalent to the reciprocal of the positive exponent of the number. Product of Powers Property xn•xm = xn+m (x ≠ 0) To multiply two powers with the same base‚ add the exponents. Quotient of Powers Property xn xm = xn−m (x ≠ 0) To divide two powers with the same base‚ subtract the exponents. Power of a Product
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