The ultimate definition of a power, or exponent, is to raise that you multiply that number the number the number of exponents there are. For example, if you had 3 to the 2nd power, it wouldn't be 6, but instead 9, because you multiply 3 twice. The positive and negative powers are very different. If there is 3 to the negative 2nd power the answer would be much different. It would be than one, but not exactly a negative number. Another way of expressing a exponent would be using the sign known as the carrot. The carrot isn't just used for math, but used for grammar too, especially if you want to make a correction somewhere inside your essay. The carrot has the same effect in math, but instead of using it for grammar, it depicts where the exponent goes. 7^2 power would mean exactly 7 to the 2nd power. 
             The number wouldn't exactly be a negative if you multiplied it be a negative exponent, because your not multiplying that number negative times. Instead, the solution would be to go into the process of multiplying negative exponents. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x–2" (x to the minus two) just means "x2, but underneath, as in 1/(x2)".

• Anything to the zero power is "1", so 00 = 1.
• Zero to any power is zero, so 00 = 0.

              Exponents are used in most maths, especially algebra. Exponents are known to put a number in "the power of" something. For example, if you had 4 to the 2 power, you would multiply 4 times 4 and come up with 16. You wouldn't multiply 4 times 2, because and exponent is the same number multiplied by 2. If you have any number to the 2nd power, it's called square, and if you have and number to the 3 power it would be known as cubed. Exponents can appear anywhere in real life, and is a simplified version of long multiplying. You can only use exponents if the number is the same.
               If you had 4x4x4x4x4x4x4x5 you wouldn't say 4 to the 8th power, but instead 4 to the seventh power times 5. If The reason for exponents is also to shorten the equation, or expression. Exponents can be seen or used anywhere, but especially in most complicated mathematical equations. Having the power of exponents can have a great impact on shortening an equation. If, however, you have a negative power, you take the who thing, the number and the negative power, and you put a 1 over it. Then your equation should look something like 1/6 to the negative seventh.