Any number to the 1st power is the same number, unchanged. Two to the 1st power is 2.
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One half to the negative first power is equal to the reciprocal of one half raised to the first power. The reciprocal of one half is two, so (1/2)^(-1) = 1 / (1/2) = 1 * 2 = 2.
A negative power/index/exponent simply inverts the expression and the power now becomes a positive number. 2-1 = 1/21 = 1/2 = 0.5 Note : This also applies if the term is the denominator. For example : 1/3-2 = 32 = 9.
2-1 = 1/(21) = 1/2 = 0.5
A similar question can be solved as below : If x to the power 4 plus 1 upon x to the power 4 equals 23 then what will be (x minus 1 upon x) to the power 2 equals what?a2 + b2 = (a + b)^2 - 2ab.so (x^2 )^2 + (1/x2)^2 = (x^2 + 1/x^2)^2 - 2 = 23.so (x^2 + 1/x^2) = 5.therefore(x - 1/x)^2 = (x^2 + 1/x^2) -2 = 5 -2 = 3.
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