Things That Go Bump(ed)… to a New Power

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Maybe it’s just me, but I don’t understand people who don’t understand exponent rules. Sure, there are rules, and sure rules can easily be confused or forgotten, but these rules are just so common sense. In fact, they make so much sense that you could completely forget that they ever existed and get along just fine.

 

Let’s not worry about the rule here. Let’s just consider what exponents are. Three raised to the seventh power just means 3*3*3*3*3*3*3. What does squaring something mean? It means multiplying something by itself. So, if we have three times itself seven times, and then seven more threes added to that string of multiplication. That gets us fourteen threes, or three to the fourteenth power.

 

Let’s take another example.

 


 

Again, don’t worry about remembering the rules. What does this really mean?

 

 

Simple canceling will get rid of three pairs of fours, leaving us with two, or four squared.

 

Let’s be honest: if you’re going to be successful on your test, you’re going to have these exponent rules memorized by the time that test day rolls around. But, that’s really due primarily to the fact that you will have used the rules so many times in practice that a comfort level will develop, NOT because you locked yourself in your room and memorized rules.

 

And the comforting fact remains, as long as you understand the most basic idea of exponents, even if you blank out on test day, you should always be able to figure out exponent problems.

quantQ
 Glow In The Dark Algebra

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Not all GMAT problems have to be boring. In a word problem, they can introduce sports, fast cars, celebrities, rock and roll, or even radioactive materials. Enjoy the diversion, but put it aside to focus on the numbers you’ve been given.

Question of the Day

The weight of a radioactive metal reduces by half every 1 second. If an experiment starts with grams of the radioactive metal, which of the following expressions gives its weight in grams, after  minutes?

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Some people think in the form of equations. Most of us don’t. But, by thinking about what will happen after one second, then after two, and three, and so on you give yourself an opportunity to see the pattern that will help you discern what the equation should be.