GRADE 7 MATHEMATICS Quarter 2 Week 1 Laws of Exponents

hello good day everyone my name is teacher ivan and today we will study about laws of exponents for multiplication and it is called the product law but before we proceed do not forget to like share and hit the subscribe button and notification bell for updates about our latest videos so let us start with our objectives for today at the end of this video we will be able to discuss the importance of following the laws of exponents next is we apply the steps and the rules in answering laws of exponents for product law and last we have to understand the importance of obeying simple rules or laws inside and outside your home so let us kick this off by knowing first the definition of law and exponents so when we talk about law it is a system of rules created and enforced through social or governmental institution to regulate behavior okay so meaning to say these are the standards that we have to follow in order for us to be organized and civilized when it becomes math these are the rules that we have to consider before making any steps okay so next is exponents so when we talk about exponents it denotes number of times you multiply the base to itself so most often than not we tend to multiply the base to its exponents but mind you that is the common mistake of most of those of the students allow me to demonstrate by giving you examples so the first example is 5 raised to the second power or 5 squared so what we usually do is do we just simply multiply 5 by 2 which is the common mistake okay so we should what we should do is we multiply 5 times 5 and that will be equal to very good it's 25 okay next let's have some more examples okay so next one is 3 cube or 3 raised to the third power okay so three raised to the third power what we what other students usually do again is you we multiply three times three well that is incorrect okay so what we should do is we multiply three by itself three times so it should be three times three times three and the answer will be correct it's 27. all right now let's uh go to the next example that will be the last example for our exponents okay so we have two raised to the fifth power so when we talk about two raised to the fifth power what we do usually is 2 times 5 well again do not do this ok so what we should do is you multiply 2 times 2 times 2 times 2 times 2 and that will give you what great that's 32 all right perfect now that we already know the definition of tho of both words let us combine both and discuss the product law so when we talk about product law it states that if a is raised to the m power times a raised to the n power where a are your bases and m and n are your exponents what you what we usually do is just simply copy the base a and add the exponents but what if there is but what if there is a numerical coefficient so we have to follow this three simple steps so the first one is we have to multiply the numerical coefficient after multiplying the numerical coefficient we copy the base and then add the exponents okay so to further understand this let us have some examples example number one x squared times x to the fifth okay so what we are going to do first is to follow the steps all right now multiply the numerical coefficient it shows here that there is no numerical coefficient present so always remember that if there is no numerical coefficient beside the variable the value is always one okay so again if if the numerical coefficient is not present the value of the numerical coefficient is always one so what you're going to do is to multiply the numerical coefficient one times one so the answer will be one right and then proceed with the second step which is copy the base and the base is x okay and then what you're going to do next is to add the exponents so two plus five that will give you seven all right so again since uh the numerical coefficient is one you don't have to write it down okay so same with exponents if the expo if the exponent is one you don't have to write it down okay now let's proceed with number two number two we have three x to the eighth times four x to the fifth so again follow the simple steps the three steps first is you multiply the numerical coefficient based on the example we have the numerical coefficient which is three and 4. so multiply that you will have 12. okay the next step is to copy the base which is x so copy the base x and then add the exponents eight plus five that will give you thirteen getting it all right perfect now let's have number three example number three we have negative five x squared times seven x cubed so basically as you can see in this example the signs of the numerical coefficient are different so remember this song whenever you are multiplying i i actually created this song before when i was in college so it's go it goes like this same sign positive when we multiply different sign is negative as well when we divide so basically if it's the same sign it should be positive and if it is different sign it should be negative so basically here on this example number three we have different sign so the the product should be a negative so negative 5 times 7 will be equal to negative 35 okay then copy the base x and then add the exponents two plus three that will give you five okay getting it okay now let's have another example number four so for number four we have negative six x to the seventh times negative nine x to the fourth so in here we have similar signs or same signs so the product will be positive so 6 times 9 will give you positive 54 all right and then copy the base x then you add the exponents seven plus four will give you eleven all right got it let's have one last example number five oh okay you can see here that we have two bases or two variables x and y so let's try it out shall we okay now let's multiply eight times negative nine so 8 times negative 9 since they have different signs you will have a product which is negative so 8 times negative 9 will give you negative 72 all right next is we will we will proceed with the next step which is copy the base and the base the first base is x and then at the exponents of x we have seven plus five the answer will be twelve and then go back to the next step which is copy the base y and then add the exponents four plus six you will have ten so that is already the answer got it all right perfect now let's have some more examples shall we okay so what if we have different bases so let's have some examples so the first step here we are going to do is we multiply the numerical coefficient the next thing is to copy the base and then copy the exponents so the only difference between the two the previous steps that i have explained earlier is that on the third step of this one we are going to copy the exponents so let's have example number one so first you have your x squared times y to the fifth okay so you've noticed that the bases are different okay so let's uh go over with the steps shall we all right now first multiply the numerical coefficient so since the numerical coefficient is not present we will have one times one the product will be one okay and then copy the base x and y okay and then third step is you to copy the exponents two and five all right so since you don't have to write down the one so you'll just simply remove that one okay so the final answer is x squared y to the fifth okay now let's have one more example two x cubed times four y to the sixth following the steps we have multiply the numerical coefficient two times four will will have eight and then copy the base x copy the exponent three then copy the base again y then copy the exponent six easy right so let's have number three so number three we have negative seven x to the fifth times six y to the eighth so you've noticed that the signs are different so the product should be a negative so negative 7 times 6 you will have negative 42 and then copy the base x and its exponent which is 5 then copy again the base y then the exponent eight all right now let's have some more okay so combining all the skills that we have discussed earlier let us try some more examples okay we will mix it up so number one 2x squared times 3x cubed y to the pip so in here you've noticed that the first uh factor doesn't have a y meanwhile the second factor has a y so we'll just go on with the with the steps shall we perfect now let us multiply the numerical coefficient 2 times 3 so the answer will be 6 right and then copy the base x then add the exponents 2 plus 3 will give you 5. and then since y is doesn't appear on the first factor we'll just simply copy it y to the 5th got it all right let's have number two okay so negative six x to the fourth y to the sixth times five x squared y to the eighth z so you've noticed that um on the first factor we have x and y you know on the second factor we have x y z so again we'll just continue with the process or the steps so negative six times five we'll have negative thirty and then copy the base x then add the exponent 4 plus 2 you'll have 6. then in y just copy y then add the exponent 6 plus 8 will have 14. and since there is no z on the first factor we'll just simply copy the letter z but take note that z always has an exponent of 1. all right but it you don't have to write it down just like in the numerical coefficient now let's proceed with number three okay so for number three we have nine y to the 6 z times negative 4x to the fourth y to the fifth z squared so we've noticed that on the first factor we just you don't have x okay so let's just go on with the the steps shall we okay 9 times negative 4 we'll have negative 36 and then since we don't have x on the first factor we'll just simply copy the base and its exponent x to the fourth all right then we have y copy the base y and then add the exponent six plus five we'll have 11. and last we have z times z squared okay so z the first z has an exponent of one so we will just simply add one plus two that's why it's three all right got it okay so now let's have some exercises i believe you can do it right okay so let's have some exercises shall we all right so let's answer number one okay for number one we have nine x to the fifth times seven x squared so in here you just simply first multiply the numerical coefficient and the product will be okay perfect it's 63 that's good now copy the base and what will be your base okay that's correct it's x and then add the exponents five plus two the answer is all right that's correct it's seven so the final answer will be 63 x to the seventh okay so let's have number two so for number two we have negative six x squared times negative six y to the fourth so basically you have similar or same sign so the product should be yes that's correct it should be positive so positive 36. now notice that there are different variables for different bases so what we are going to do is suggest what okay copy the base and exponent so let's do it x squared okay copy the base and the exponents and then y to the fourth got it okay perfect now let's have number three so number three we have four x squared times negative eight x y cubed so in here again we multiply the coefficients the numerical coefficients 4 times negative 8 you'll have correct it's negative 32 and then copy the base x and then add the exponents 2 plus 1 the answer is three that's good and then since why the since there's no y in the first square in the first factor so we will just simply copy the base and exponents then number four we have negative seven times three x squared y to the eighth so let's just simply multiply negative seven times three the answer is okay correct it's negative 21 and since the first factor doesn't have any variable and exponents we'll just simply copy the variables and exponents got it okay last exercise number five we have 5x cubed z to the fourth times negative two x to the seventh y to the sixth so go with the process once again five times negative two will have negative ten very good and then copy the base x and then how about the exponents add the exponents right okay so 3 plus 7 will give you 10 okay very good now since there is no y in the first uh factor what we are going to do is to just simply copy y and it and the exponent six and then same with z it doesn't have any z on the second factor so we'll just copy z and then the exponent of four got it did you get the same answers all right perfect so i have a question for you all right so what are your takeaways in this lesson what have you realized while answering the loss of exponents was it hard for you is it really hard to you know follow some rules and regulations well personally my takeaway in this lesson is that whenever we follow the rules and obey the laws we cannot we can most likely get what we want in life these laws can make us feel safe and secured always remember that if following simple rules or laws will be hard for you how long do you think it will be before you're out there breaking laws all right okay so that's it for today thank you for watching and see you next time for our other videos goodbye

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Length: 19min 48sec (1188 seconds)

Published: Sun Feb 07 2021