What is the volume of a cube of edge length five 𝑥 squared 𝑦 squared centimetres?
Here, we have our cube with edge length five 𝑥 squared 𝑦 squared centimetres. The volume of a cube is equal to 𝑆 cubed. You can also think of it as length times width times height. But for a cube, all of these are equal. They’re all the same. So you can just let it be this side cubed. So we write it as 𝑉 equals 𝑆 cubed. The volume equals a side length cubed.
So let’s go ahead and replace 𝑆 with five 𝑥 squared 𝑦 squared. And then at the end, remember to add our units. So we’ll need centimetres cubed. So volume equals five 𝑥 squared 𝑦 squared cubed. To find the power of a product, find the power of each factor and multiply.
So essentially, let’s go ahead and write this out three times because when you cube something, you’re multiplying it to itself three times. And then we’ll put the factors together — the like bases together. Now that we’ve written it out three times, let’s go ahead and put our factors together.
So now we can multiply with like pieces and when you do that, you can just add your exponents. Keep in mind that each of these fives have an exponent of one. So we will have five to the one plus one plus one, 𝑥 to the two plus two plus two, and 𝑦 to the two plus two plus two. Adding the ones together, we now have five cubed. Adding the twos together, we have 𝑥 to the sixth. And adding the twos together, we have 𝑦 to the sixth.
Five cubed is 125 times 𝑥 to the sixth times 𝑦 to the sixth. Now since this is a volume, we need to add our units centimetres cubed. So the volume of a cube of edge length five 𝑥 squared 𝑦 squared centimetres would be 125𝑥 to the sixth 𝑦 to the sixth centimetres cubed.