Become a P.E.R.T. ex-pert.
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What's Inside Shmoop's Online Math P.E.R.T. Test Prep
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Simplifying expressions is a bit like following the rules of etiquette. It's not against the law to chew with your mouth open—but come on. It's gross. Similarly, writing y4 instead of 4y isn't wrong; it's just not nice. There are a few rules of mathematical etiquette that everyone's agreed to, and they make the math world a non-gag-reflex-inducing place.
Sometimes those rules are obvious. Everyone agrees that 6x2 is simpler than (5x2 – x2 + 8x2 – 6x2). Other situations aren't so obvious. Take square roots. For square roots to be in simplest form, no perfect square factors can be left under the radical.
In , for example, 16 is a perfect square factor of 32 and x2 is a perfect square factor of x3. Etiquette says they must move out from under the radical and make space for the non-perfect factors. is considered to be simpler than even though they both take up the same number pixels on the computer screen.
Another convention with expressions containing radicals is that the radical is written at the very end of the expression. Typically, people write , not , because it's hard to see exactly where the radical ends. Is the 4x supposed to be under the radical or not? To prevent confusion, shuffle the 4x out front.
For expressions with exponents, the simplest form includes no negative exponents. x2y -3 isn't considered fully simplified; it should be written . All factors with the same base should be combined so that bases aren't repeated. z3z5, for example, can be simplified to z8. z3z5 gets the point across, but leaving the variables uncombined is simply not done. Writing it that way is like using the lobster fork to eat the shrimp. It's not that it doesn't work; it's the looks of condensation from other mathematicians.