welcome to math with Mr J [Music] in this video I'm going to cover what squaring and cubing a number means so how to square a number and how to cube a number now simply put when we square a number we multiply a number by itself when we cube a number we multiply the number by itself three times when we see an exponent of 2 that means we are squaring a number when we see an exponent of 3 that means we are cubing a number let's jump into our examples and see exactly what this looks like starting with numbers 1 and 2 where we will take a look at how to square a number and then we'll move to numbers three and four where we will take a look at how to cube a number for number one we have 4 squared whenever we are working with exponents the bigger number to the left is called the base so for number one this 4 is the base the smaller number to the right is called the exponent so this 2 is the exponent for number one whenever we see an exponent of 2 we are squaring a number and we can say that number squared for example number one we can say this as 4 squared now 4 squared means four times four let me rewrite this underneath here so 4 squared equals 4 times 4 we take that base of 4 and expand it out two times four times four that equals 16. so 4 squared equals 16 and it's as simple as that now a common mistake when working with exponents is to multiply the base by the exponent for example in number one four times two would equal 8 and would be incorrect so again don't multiply the base by the exponent expand the base out however many times the exponent tells you before we move on to number two I do want to mention why we call it squaring a number if we take a look at a square we can see why we call it squaring a number for example if we were to take a look at a square with side lengths of four we can find the area of this Square by doing four times four or four squared that gives us an area of 16. we can square a side length to find the area of a square so you can see the relationship between squaring a number and the area of a square squaring a number or squaring a side length gives us the area of a square let's move on to number two where we have 7 squared now 7 squared that equals or means 7 times 7. expand that base of 7 out twice seven times seven equals 49 so 7 squared equals 49 that's how we square a number let's move on to cubing a number starting with number three where we have 4 cubed so anytime we have an exponent of three we are cubing a number now again when working with exponents the bigger number to the left is called the base so this 4 is the base for number three the smaller number to the right is called the exponent so this three is the exponent for number three that three tells us to expand the base out three times and multiply that number by itself three times let me rewrite four cubed down below here so 4 cubed means or equals four times four times four take the base of 4 and expand it out three times four times four equals sixteen times four equals sixty four four cubed equals sixty four now again avoid the mistake of multiplying the base by the exponent so for number three four times three would give us 12 and that would be incorrect expand that base out however many times the exponent tells you before moving on to number four I do want to mention why we call it cubing a number so let's take a look at a cube for example if we were to take a look at a cube with Edge lengths of 4 we can find the volume of this Cube by doing length times width times height which would be 4 times 4 times 4 which is just 4 cubed we can Cube an edge length to find the volume of a cube so you can see the relationship between cubing a number and the volume of a cube cubing a number or cubing an edge length gives us the volume of a cube let's move on to number four where we have 7 cubed now 7 cubed equals or means 7 times 7 times 7. expand that base of 7 out three times seven times seven is forty-nine times seven equals 343 so 7 cubed equals 343 so there you have it there's how to square and how to cube a number I hope that helped thanks so much for watching until next time peace foreign