Write a monomial that is equal to the area of this square.
The area of a square can be written as length times width. The length and the width are the same because it’s a square, and all sides are equal on a square. So three 𝑎 to the ninth 𝑏 to the fourth will be our length and our width. So our area will be three 𝑎 to the ninth 𝑏 to the fourth times three 𝑎 to the ninth 𝑏 to the fourth.
In order to multiply powers with the same base, we need to add their exponents. So before we do that, let’s go ahead and put the like bases together. So now that we have our like bases together, we can add their exponents. Three to the first times three to the first, so here we need to add one plus one because we have the same bases of three already together. Next, we will have 𝑎 to the nine plus nine and 𝑏 to the four plus four. Let’s simplify. So we have three squared times 𝑎 to the eighteenth times 𝑏 to the eighth resulting in nine 𝑎 to the eighteenth 𝑏 to the eighth.
So the area of this square would be nine 𝑎 to the eighteenth 𝑏 to the eighth.