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Power Equations and Calculator Inputs Power Equations The solution to the equation x 3 = –8 is x = √–8 = –2. 3 Using fractional exponent notation, we write these steps as if x 3 = –8 then x = (–8) 1/3 = –2. (Rational) Power equations are equations of the type x P/Q = c. To solve them, we take the reciprocal power, that is, if x P/Q = c, then x = (±) c Q/P. Note that x P/Q may not exist, or that sometime we get both (±) x P/Q solutions means that sometimes. The reciprocal of the power P/Q The reciprocal of the power 3
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Power Equations and Calculator Inputs Example A. Solve for the real solutions. a. x 3 = 64 x = 64 1/3 or that 3 We note that this is the only solution. x = √64 = 4. b. x 2 = 64 x = 64 1/2 or that We note that both ±8 are solutions. x = √64 = 8. c. x 2 = –64 x = (–64) 1/2 which is UDF. (In fact what most calculators return as the answer meaning that there is no real solutions.) d. x –2/3 = 64 x = 64 –3/2 x = (√64) –3 = 4 –3 = 1/16.
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Power Equations and Calculator Inputs Finally, for linear form of the power equations, we solve for the power term first , then apply the reciprocal power to find x. e. 2x 2/3 – 7 = 1 2x 2/3 = 8 x 2/3 = 4 x = 4 3/2 x = (√4) 3 = 8. We note that actually both ±8 are solutions.
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