Mastering Algebra - Working With Exponents - Part I

Exponents - Mastering Algebra - Working With Exponents - Part I

Hello everybody. Now, I discovered Exponents - Mastering Algebra - Working With Exponents - Part I. Which may be very helpful if you ask me so you. Mastering Algebra - Working With Exponents - Part I

Mastering algebra requires that the pupil be cognizant of the properties of exponents. Exponents occur repeatedly in algebra and nothing else but in all higher branches of mathematics. Here in this series of articles we discuss what an exponent is and how to deal with and simplify expressions curious powers.

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Exponents

An exponent is the power of a whole or expression. For example 3^4 (in which the "^" caret stamp represents exponentiation, or the raising to a power), the whole 3 serves as the base, and the 4 after that extra caret stamp tells us how many times to use 3 as a factor when multiplying by itself. Thus 3^4 means 3x3x3x3 = 81. Thus the exponent serves as a suitable shorthand notation to indicate repeated multiplication using the same whole as multiplicand.

It is very easy to simplify expressions curious exponents, whether these be purely numerical examples as in (3^4)(3^2), or algebraic examples such as( x^3)(x^4). When the base is the same and we are multiplying expressions curious exponents, we naturally add the exponents and keep the base. Thus in (3^4)(3^2), we do 4+2 = 6 and thus this expression becomes 3^6. In ( x^3)(x^4) we have 3+4 = 7 and thus this expression becomes x^7. If it is not positive why we would add exponents together in such expressions, just think of the exponent as signifying beads on a necklace. If you string together 3 beads and then 4 beads, as in the second expression above, you have 7 beads.

If you have an expression in which you raise an exponential expression to an additional one power, you naturally multiply the exponents of the expression. Thus in (x^4)^2, you multiply the 4 and 2 to get 8, and end up with x^8. To understand why this is so, you need to recall that the exponent 2 in this example applied to the x^4 expression, tells us to use that twice to multiply itself. Multiplying x^4 by itself gives us x^8, as now we can use the rule learned in the previous paragraph. If you break things down this way and understand not only how but why, you are then in a much better position to make serious strengthen in algebra.

Two other key properties of exponents that you need to know are the following: 1) When you raise anything to the first power you accumulate the given quantity; thus 3^1 = 3 and x^1 = x. This 1-exponent is also an imperceptible demon in the sense that even though we do not generally write the "1-exponent" it is always there understood. This is prominent to understand in examples such as x(x^5), which is nothing else but (x^1)(x^5) and thus equals x^6; 2) Any expression to the 0th power is equal to 1. Thus x^0 = 1, and 4^0 = 1.

In the next part of this article, we shall peruse the distributive and division properties of exponents. Once you get all the properties down pat, you will never again be at a loss with exponents; and since you will invariably come across exponents in all aspects of mathematics, having a mastery of this aspect will insure your continued success in this discipline.

I hope you receive new knowledge about Exponents . Where you'll be able to offer used in your day-to-day life. And most importantly, your reaction is passed about Exponents .

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