Learn about Numbers in Exponential Form We’ll learn about how to express numbers in exponential form. There are two questions. The first question asks us which of the given expressions has the smaller value or the smallest value. So, we’re given three expressions. Let's write them down. The first question says, the expressions are 23, 30 or 1021. So two 23, how do I compute the value? This is the same as 2 x 2 x 2. Essentially what I did is I look at the base which is right here, this is called the base and this is called the exponent. So I take the base and multiply it into itself three times; 2 x 2 x 2 which is 8. So that’s the first value. The value of 30 is always one because anything could be power or when the exponent is zero, it's one. We have to remember is the exponent equal zero, the value equals one. Now let's look at the third number which is 1021 which means I just write 102 and multiply it by itself one time. So the answer is 102. So the three numbers or the three exponents are 23, 30 and 1021 which means I am comparing the values of eight, one and 102. Obviously, this has the smallest value. So the smaller value is 30. That’s the answer. That’s the smaller or smallest value. The second question asks us to write this equation 3 x 3 x 3x 3 using an exponent and find the value. So the second question wants us to write 3 x 3x 3 x 3, what is the value and to write it in exponent form? Let's do that. Let's create a little bit of space and by the way, this period is the same as multiplication. So, 3 x 3x 3 x 3 = 3 x 3 is 9 x 3 is 27 x 3 is 81. So the value I know is 81. That was easy to determine. Now in order to write this in exponent form, I do this. I simply look at the base. The exponent form is base and exponent. This is how we write it. The base is the number which is being multiplied by itself. The exponent equals number of times it is multiplied. So in this case, the base is the number three and the exponent is how many times am I multiplying three? Well that’s one, two, three, four times. So I can simply write this down as 34. So what have we looked at when we look at the question? The first question, let's see what we've learned. What we've learned is; if I have been given three different exponents, I can compare them by computing the value of each one of them and the way I compute the value is I take the base, multiply it by itself, the number of times of the exponent. So if the exponent is three, I multiplied the base which is two three times, 2 x 2 x 2 gives me eight. 3 x 0, any base which is multiplied itself zero times will give me the value of one. And 1021 or exponent of one is 102. Since I have all three in whole numbers, I can compare the value and I know simply that one has got the least value. So 30 is the smallest of the three. Now, in the reverse case; what I'm given is 3 x 3 x 3 x 3 and I have to express this in exponent form, I can simply compute what is the base and what is the exponent. The base is the number being multiplied which is three and the exponent is the number of times it's multiplied which in this case is four times. The value of that is 81.