 Hello friends, so welcome to a new session on mathematics and in this the following series of sessions We are going to deal with Exponents of real number what exactly are exponents and why are they required everything will be discussing? So this particular session and the series of the sessions which are going to follow Would be very very important for you to develop good mathematical foundation because going further Exponents and indices will be used a lot many times in multiple areas of mathematics Now to begin with let us consider these two data points now It's given that speed of light, you know light and you must be aware that light travels at a speed of This much right so the number is so big that you know even to Count the zeros will be you know Difficult so if you see how many zeros following three it's around three double zero triple zero triple zero so around 300 million meters per second Right 300 million Isn't it so Yes, so basically it is three lakh kilometers per hour Sorry three lakh kilometers per second or it is 300 million meters per second. Okay. Now similarly radius of the earth is 6400 kilometers which is equivalent to six four double zero triple zero meters Okay, now if you are let's say if you are doing a calculation Related to speed of light in physics and every every time you are to Mention the value it will be too cumbersome to write three followed by eight zeros instead of that if you closely observe three followed by Eight zeros can be written as three into one followed by eight zeros. Isn't it? This is how you can write right three followed by Three into one followed by eight zeros now here this particular value one followed by eight zeros Can be shorthand written as ten to the power of Eight yeah ten to the power eight which is nothing but ten multiplied by Ten how many times? eight times so if you see Isn't it one two three four five six seven so if you see there are eight times ten is being multiplied so whenever such Mathematical calculations are happening. We have a new notation and which is written as ten and there is a superscript over it Which is here in this case. It's eight, which means Then when multiplied by itself eight times can be shot written in shorthand like this, right? This is a new notation Similarly, let us say if I had to write radius of the earth So radius of the earth is 64 or six point four if you are aware of decimal operation It is one followed by six zeros Six zeros if you see this is this is nothing but one million and one million can be written as ten into ten into ten how many times Six times is it it so we take advantage of this repetition and We have now coined a new notation where we write ten and superscript as six so this becomes ten and we read it as ten raised raised to power Six power six. This is how we then raise to power six. This is how we define Indices now. So what is it? So any number? Let us say two when multiplied five times So two into two into two into two into two. This is two multiplied by five times can be written as To raise to the power five now here Two is called the base. What is it called the base and Five has multiple names one. It can be called as exponent Exponent it can also be called as index whose plural is in dices and Third is power So you can call it by any name isn't it now To and the base and the exponent the base and Exponent and Exponent can be can be any real numbers can be any Real Numbers except in few cases where negative bases are not allowed Except in a few cases where negative bases are not allowed Also, there are a few cases where also zero in few cases as base zero as base is Is Not allowed Not allowed and specially the case of zero to the power zero. We'll see this is not allowed in Mathematics, so you hope you understood so now Generalizing I can say a to the power B. So this type of number whenever you encounter so what is a here a is the base and B is the index or the exponent Okay, so now in the next session, we'll be dealing with laws related to bases and exponents