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# dq2 - Quotient Law a^m a^n = a^(m n LHS = a^m a^n =(a a …...

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Post a response to the following: Review section 10.2 (p. 692) of your 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. Rule Explanation Examples Product Law a^m * a^n = a^(m + n) LHS = a^m * a^n = (a * a * … m times) * (a * a * … n times) = (a * a * …) (m + n) times = a^(m + n) = RHS 3^7 * 3^2 = 3^(7 + 2) = 3^9 5^a * 5^b = 5^(a + b)
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Unformatted text preview: Quotient Law a^m / a^n = a^(m - n) LHS = a^m / a^n = (a * a * … m times) / (a * a * … n times) = (a * a * …) (m - n) times = a^(m - n) = RHS 4^7 / 4^2 = 4^(7 - 2) = 4^5 m^3 / m^-2 = m^[3 – (-2)] = m^5 The laws work with rational exponents in the same way that they work with integer exponents. For example, a^(1/p) * a^(1/q) = a^(1/p + 1/q) = a^{(p + q)/pq} and a^(1/p) / a^(1/q) = a^(1/p - 1/q) = a^{(q - p)/pq} A third example for classmates to solve can be: Simplify the expression 2^(1/8) * 2^(1/12) The Answer is: 2^(1/8 + 1/12) = 2^(3/24 + 2/24) = 2^(5/24)....
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