An exponent can be a positive number, a negative number and even a value of “zero”. If you are provided with exponents in fraction or a value of p/q for example y4/y3, you can solve it up as y4-3= y1=y. As I told you earlier that an exponent can be either a value of positive number, negative number or even zero; it is never a sure show probability that the examiner will only put forward a value in form p/q in front of you and instead he may even put forward zero or negative exponents in front of you. In order to be able to solve such exponent types, the following tips can be bought in use:-
How to Solve Zero and Negative Exponents
1. Solving the zero exponents:-
We always take the value for a zero exponent as 1 and, I can explain why. Suppose there is an exponential equation with zero value before us. i.e. y4/y4 and we know that when we solve this equation, we will get the answer as y4-4=y0 but y4 always equals to y*y*y*y where *sign stands for multiply and thus when we divide y*y*y*y by y*y*y*y, we get the value as 1 as something divided by something always equals to one and this is why we always take the value for zero exponents as one and here x is never equal to zero.
2. Solving the Negative Exponents:-
Suppose a negative exponent is given to you for example 8-1, you can easily solve it by taking it as 1/8. If instead you would have been given a value 10-1, it would have resulted as 1/10. Actually, while solving the negative exponents, the negative value of power gets positive when we apply it downside as a denominator and a positive value downside always becomes negative when we take it upside applying it with the numerator.
3. A Sample Solution:-
Suppose someone asks you a question, “Simplify: (84)0 * 4-1 where * stands for multiply. The initial part of this question includes a zero value of exponent while the final value includes a negative exponent and we can apply both the rules mentioned in above two points here in this equation to solve it. i.e. (84)0 * 4-1 = 1= 1.1/4=1/4 answer.
4. Ending the Catharsis of Values:-
I make Mathematics as simple here for you while solving the exponential values as here you just have to keep two things in your mind. The first one is to subtract the powers when you get them with the same exponent in the form of p/q and second is to take value of zero exponents as “1” and value of negative exponent as the inverse value of the same number.
5. Keep in Mind the Identities:-
The teacher will keep on telling you some identities based on the same topic when he teaches the chapter of exponential values. Just cram these values or write them on a spare piece of paper while solving the questions and you will soon be able to solve even the most complicated questions of the same chapter.