Learn about Exponential Form In this lesson, let’s talk about writing numbers in exponential forms. We are given two problems. Let’s do them one-by-one. The first problem question says for us to arrange the following numbers in order from the least to the greatest. So the numbers are 25 or the base of two would be exponent of five, 33, 9, 52 and 81. So if you need to ask arrange them in order from lowest or least to the greatest, let’s calculate the values of all of them. So 25 is the same as 2 × 2, I’ll multiply a two five times. What is this? 4, 8, 16, 32. Let’s try the other one. 33 = 3 × 3 × 3 = 27. 9, it’s easy, it’s 9. 52 is 5 × 5 which is 25. Last one is 81 = 8. So now that we have these in value, we have the values of all of them, it is easy for me to arrange them. So this is the greatest, which is the lowest? Well this is the lowest, this is the second lowest. Then we’ve got 25 then 27 then 32. So it should be in this order. So the orders are, well first is 81. Next is 9 which is less than. Third is 25 which is 52, which is less than 33, which is less than 25. That’s the order that we were looking for. All we did was compute the values for all five numbers. Now let’s try the second one. One says to write 81 in two different exponential forms. What they mean is two different bases. So we have to write 81 in exponential form. We need to write 81 in the form, exponential form. So 81 can be written as 9 × 9. The idea is to break it down so I have the same number being multiplied repeatedly. 81 = 9 × 9, which means it’s a base of 9 and because it’s being multiplied twice, the exponent is two. The second is 81 can also be written as – I can break 9 as 3 × 3 × 3 × 3. So it’s the same base which is 3 repeated four times, so 34. Since I can write 81 as two different ways, it is 92 or 34. So in two different forms, it is 92 or 34. That’s the answer we were looking for.