Mastering algebra requires the student to be aware of the properties of exponents. Exponents appear repeatedly in algebra and, indeed, in all higher branches of mathematics. Here in this series of articles, we discuss what an exponent is and how to handle and simplify expressions involving powers.
Year exponent is he Energy of a number or expression. For example 3 ^ 4 (in which the “^” caret symbol represents exponentiation, or elevation to a power), the number 3 serves as the based, and the 4 after that special caret The symbol tells us how many times to use 3 as a factor when multiplying by itself. Therefore 3 ^ 4 half 3x3x3x3 = 81. Therefore, the exponent serves as a convenient shorthand notation to indicate repeated multiplication using the same number as multiplying.
It is very easy to simplify expressions that involve exponents, whether they are purely numerical examples as in (3 ^ 4) (3 ^ 2), or algebraic examples like(x ^ 3) (x ^ 4). When the base is the same and we are multiplying expressions involving exponents, we simply add the exponents and retain the base. So on (3 ^ 4) (3 ^ 2), we make 4 + 2 = 6 and therefore this expression becomes 3 ^ 6. On (x ^ 3) (x ^ 4) we have 3 + 4 = 7 and therefore this expression becomes x ^ 7. If it is not obvious why we would add exponents in such expressions, just think of the exponent as a string of beads. If you string 3 beads and then 4 beads, as in the second expression above, you have 7 beads.
If you have an expression where you raise an exponential expression to another power, simply multiply the exponents in the expression. So on (x ^ 4) ^ 2, multiply 4 and 2 to get 8, and end with x ^ 8. To understand why this is so, you must remember that the exponent 2 in this example was applied to the x ^ 4 expression, tells us to use it twice to multiply. Multiply x ^ 4 by itself it gives us x ^ 8, since now we can use the rule learned in the previous paragraph. If you break things down this way and understand not only as objective why, then you are in a much better position to make serious progress in algebra.
Two other key properties of exponents you need to know are: 1) When you raise something to the First power you get the given amount; Thus 3 ^ 1 = 3 Y x ^ 1 = x. This 1 exponent it is also a invisible demon in the sense that although we generally don’t write the “1 exponent“is always understood there. It is important to understand this in examples like x (x ^ 5), which is really (x ^ 1) (x ^ 5) and therefore it is the same x ^ 6; 2) Any expression to 0ยบ the power is equal to 1. Therefore x ^ 0 = 1, Y 4 ^ 0 = 1.
In the next part of this article, we will explore the distributive Y division properties of exponents. Once you have mastered all the properties, you will never miss the exponents again; And since you will invariably meet exponents in all aspects of mathematics, mastering this aspect will ensure your continued success in this discipline.
