Question 179117
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*[tex \Large (x + 3)^{-1/3} = -1]


Negative exponents signify the reciprocal and fractional exponents signify roots, so the following is an equivalent equation:


*[tex \Large \frac {1}{ \sqrt[3] {x + 3} } = -1]


Just raise each side to the 3rd power:


*[tex \Large \frac {1}{x + 3} = -1^3 = -1]


Multiply both sides by <i>x</i> + 3:


*[tex \Large -x - 3 = 1 \rightarrow x = -4]


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*[tex \Large 25^{3 \over 2} = (sqrt{25})^3 = 5^3 = 125]


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*[tex \Large x = sqrt{1 - 8x} + 2]


Add -2 to both sides:


*[tex \Large x - 2 = sqrt{1 - 8x}]


Square both sides:


*[tex \Large x^2 -4x + 4 = 1 - 8x]


Add -(1 - 8x) to both sides:


*[tex \Large x^2 +4x +3 = 0]


Factor:


*[tex \Large (x + 1)(x + 3) = 0]


*[tex \Large x = -1] or *[tex \Large x = -3]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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