### GMAT Prep - Math - Algebra - Negative Bases by Knewton

Go to http://www.knewton.com/gmat/ for hundreds of GMAT math and verbal concepts, thousands of practice problems and much more. Knewton GMAT is a GMAT prep course that redefines everything you thought you knew about online learning. We can use the rules of the multiplication of negative numbers to determine the sign of a negative base raised to an exponent. Remember that a negative number times a positive number is a negative number and that two negative numbers multiplied together is a positive number. We'll use that rule again and again. Here's an example: -10 raised to the 1st power. This is -10 times 1, a negative number times a positive number, which gives us a negative number, -10. However, -10 raised to the 2nd power, or -10 times -10, is 100, which is a positive number because multiplying two negative numbers together gives us a positive product. We can summarize that to say that all 2nd powers of negative number bases are going to be positive. Say we raise it to the next power: -10 to the 3rd. -10 times -10 times -10 gives us -1000 because those two negative numbers that we multiplied earlier to get a positive number are now multiplied by a new negative number. -10 to the 4th is -10 times -10 times -10 times -10. That's two sets of two negative numbers combined to make positive numbers. So our product is positive 10,000. What this means is odd numbers of negative bases -- that is, when negative bases are raised to odd numbered powers, give us negative results. When negative bases are raised to even numbered powers, they give us positive results. Subscribe to this channel for tips, explanations, and Q&A about the GMAT and getting your MBA.

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