TenMarks teaches you how to write powers and exponents.
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Learn about Writing Powers In this lesson, let's learn how we write powers. Now, powers are the way to write an expression which is always written as a base and an exponent. The key thing to remember is the format of a power, it's written as a base and an exponent. What exactly does that mean? Well, if we want to write a number as four as the base and two as the exponent, what this means is the base is the factor and how many times it's multiplied to itself depends on the exponent. So since the exponent is two, it is 4 x 4, which if we multiply four by itself so that the total number of times we see four is twice. So that’s the theory behind the power; base, exponent and it is written as this the base, the base of four and the exponent of two. The value of here is 4 x 4 which is 16. So, two problems are given to us. The first one wants us to write the power represented by the model given here. Let's look at the model. What do we have? We have a row, two rows, and three rows, each with three dots. So we’ve got three rows of three dots each. Another way of writing that will be 3 x 3. I've got three rows each with three dots and now three times three dots. Now, if I want to write this as a power, how would I do this? Well, if I look at what we’ve learned here, we said if four is multiplied by itself twice, 2 x 4, four and four, it's used twice, 4 is the base, exponent is 2. So here, the base would be three and since it's appears twice, we write 32. So it's three with an exponent of two. Now any time we see if the exponent is two, it is squared. If it is three, it's is called cubed; just a couple of quick things to remember. The way you write the power represented by this model would be 32 or 3 with the exponent 2, base 3, and exponent 2. Let's do the second problem. It wants us to write the number as a power of the given base. So the base is given as two. We need to find the exponent. The number given to us is eight. What is the exponent? The exponent basically says how many times if I put 2x2x2x2x2, how many times will I have to use this to get eight? How many times would the base be multiplied to itself? Well, in this case eight is 2x2x2. So how many times did we multiply it, three times. So the exponent will be three which implies 8=23. So that’s the number eight or the value eight written as power with a base two.