GMAT Prep - Math - Algebra - Negative Bases by Knewton

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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.

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[kumarbhim0]

Could anyone please explain why multiplication of two (or even) numbers give us positive numbrs.

[frickfrock999]

Finally, a straight forward explanation

[arunasree2020]

Valuable lesson about negative numbers, good expression.