The number 0 on the GMAT is tricky as its properties are the trap in to which a seemingly logical solution can lead you or are often either the key to unlocking a difficult solution. Learning the properties of zero (keep in mind that it is an even number) is a crucial skill, particularly on data sufficiency problems. Even more importantly, never forget to consider zero as a potential value for a variable, as it often produces surprising results. Consider the case of zero as an exponent:
x^0 is, by definition, equal to 1. Noting the properties of exponents can help you to prove and more easily remember this useful device: take, for example, the expression x^2 * x^-2. You could rearrange this two ways:
a) (x^2) / (x^2) --> The negative exponent moves that term to the denominator
b) x^(2-2), or x^0 --> When multiplying terms with the same base, taken to different exponents, you add the exponents
Because we can prove that (x^2) / (x^2) must be equal to 1, and that the two expressions above are equal to each other, we can prove that x^0 = 1.
Now here comes the payoff - because x^0 is equal to 1, it's the ultimate in cop-out solutions to difficult problems. Say that a question asks:
For what value of x will 5^x be a factor of 2^10?
2^10 is not divisible by 5 (its only prime factor is 2), but the question might seem to necessitate you to multiply that value out, as well as some potential values of 5^x, in futility to prove that point. However, if 0 is an option, it will set the term equal to 1, which is a factor of any integer, and your work is already done.
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