Our Math Monday blog assignment for today was to explain why numbers with negative exponents come out as decimals and not negative numbers. This concept seems pretty hard to grasp at first, but it's easy to understand once you get the hang of it. 

In short, negative powers result in decimal numbers because the powers are not positive. Seems confusing, I know. When a base has a positive power, the number multiplies itself by however many the exponent calls for. However, when an exponent is negative, the number multiplies downward instead of upward, so we get a fraction, which can be written easily as a decimal. To simplify these exponents, carry them out as if they were positive powers and place the result in a fraction under 1. The negative sign only signifies that it will be a fraction. This is why 2^-5 is 1/32 rather than -32. -32 in exponential form would actually be (-2)^5. This can be figured out with a similar process. 

This concept ties in with our current math unit on exponents because we're expanding what knowledge we already had of exponents and learning new concepts and principles used in exponents. It is also "layered" with our knowledge of positive and negative integers as well as our knowledge of fractions, decimals, and how they are interrelated. 

Our Math Monday blog assignment for today was to think and write about exponents. We were to write about what they are, what they do, and how they can be applied to real-world situations.

An exponent, in short, is an easy way to abbreviate a multiplication sentence that uses the same number over and over again. The number of times the number is repeated is called a "power". The number being multiplied is called the "base". For example, 8 to the third power is actually just 8 x 8 x 8.

Exponents can not always be used. They're simply a fancier way to write repetitive multiplication equations. But in the real world, they can be useful when that situation is met. For example, if a buyer buys 3 packages containing 3 apples 3 times over the course of a week, he has bought 3 to the third power apples, or 27 apples, in a week. Exponents are usually hard and confusing, especially when they are applied to real life.  Sometimes powers and bases are mixed up and confused.

You can use the Associative Property of Multiplication when solving exponents. For example, 5 to the third power or 5 x 5 x 5 is solved as (5 x 5) x 5, or 25 x 5. The answer is 125. 

Exponents are used a lot in geometry to find the area and volumes of surfaces and objects, too.

As you can probably see, exponents are pretty easy to solve once you know how!