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14.Find x so that (- 5) ^ (x + 1) * (- 5) ^ 5 = (- 13.Simplify ((- 2) ^ 3 * (- 2) ^ 7)/(3 * 4 ^ 6) |
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Answer» 2.) (-5)x+1 x (-5)5 = 1 ⇒ (-5)x+1+5 = 1 (∵ aman = am+n) ⇒ (-5)x+6 = 1 = (-5)0 (∵ a0 = 1) ⇒ x+6 = 0 ⇒ x = -6 3.) \(\frac{(-2)^3\times(-2)^7}{3\times4^6}=\frac{(-1)^{3+7}2^3\times2^7}{3\times(2^2)^6}\) (∵ (ab)m = ambm) \(=\frac{(-1)^{10}(2)^{10}}{3\times2^{12}}\) (∵ aman = am+n and (am)n = amn) \(=\frac{1}{3\times2^{12-10}}\) (∵ (-1)10 = 1 and \(\frac{a^m}{a^n}=\frac{1}{a^{n-m}})\) \(=\frac{1}{3\times2^2}\) \(=\frac{1}{3\times4}=\frac{1}{12}.\) |
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