While I have been working on the quant section, POWERS is one of the topics that is tested and on which questions can be expected. Below are a few pointers to keep in mind with regards to the Powers that I have been able to recollect and which I have read in a few quant related articles --:
1.
Keep in mind the properties of Powers
(Addition, Subtraction, Multiplication)
2. 0 is an EVEN number
3. An even power is always positive, whether the base is positive or negative.
Eg :--
(-2)^2 = 4 and (2)^2 = 4
4. An odd power retains the base's original sign.
Eg :--
(-2)^3 = -8 and (2)^3 = 8
5.
Adding and subtracting powers
with the same base:
DON'T: add or subtract the exponents
Example: x3 + x5 ≠ x8
Do:
extract the highest common factor.
Example: x3 + x5 = x3(1+x2)
6. If you're not
sure that you factored the expression correctly, check that re-expanding the
brackets does return to the original expression. This is a method to cross-check and should be used if you have time and are unsure of your answer
7. Like terms (same
base and same exponent) can always be added/subtracted:
6a2 + 3a2 = 9a2
8. Whenever one encounters an even root in the GMAT, it only represents the positive solution. Which is why x in the quadratic equation x^2-4=0 will equal ±2, but if it is stated as only √4 then it will equal 2 alone. By EVEN Root, the statement refers to square root or 4th root,
6th root and so on.
9. In
other words, both positive and negative roots must be considered if we placed the square root
ourselves, as part of solving an equation, for example.
10. If
the root sign is already there to begin with,
it signifies only the positive root (This is a mathematical convention).
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