This blog created by Fariel Mohan is to assist MATH110D students in understanding foundational mathematical concepts.
Friday, February 1, 2008
Exponent
What is the purpose of exponent? Is a quadratic an exponent? It is said that everything in life involves some aspect of Maths, give some real life scenarios that involves the exponent aspect of mahs.
ratman an exponent simply means that you have same number being multiplied a certain number of times. Eg. if u have 2X2X2 . This can also be 2 to the 3rd power which means you multiply the number (2) three times. It is what u said. It repeats itself
Exponent is an easier method of writing the product of a reccuring number ie 3x3x3x3x3 in a simpler form of 3 to the power of 5meaning 3 multiply by itself 5 times. If you are implying a quadratic equation,the whole equation is not an exponent only the variable that is raised to a power. For a quadratic, the number is raised to the power of 2. A real life scenario could be a supermarket casher,cashing for a number of items of the same kind with the same price. Instead of punching in the same digits over and over that certain button with an exponent function encoded on the "computerized" cash register is there to use to make her job easier.
exponent simply means that you have a number which is being multiplied by itself a certain number of times.That is the number of times the base number (original number) is being multiplied by itself.
i think the word exponent refers to the power of a number. for example the number 2 to be squared or the number 2 raise to the power of 3. Exponent simply refers to the power.
Ratman i will try to answer your question to the best of my ability. Firstly an exponent is a mathematical operation. a mathematical operation tells you what particular action to take when the operation is encountered. eg. if we encounter the mathematical operation + we understand to add likewise if encounter the exponent operation we should understand that it means to multiply that number refered to as the base by the exponent (the superscript number)that number of times as stated by the exponent (again the superscript number). your second and third question reffers to the same solution.
cruiser if your question is how to work with negative exponents eg 5^-2 (5 raised to the power -2). Simply the solution is 1 divided by 5^2 i.e. 1/25 (i believe). i hope my explaination is accurate as i would not like to post inaccurate information. Could someone please clarify my explaination if necessary.
writing a number in expotent form simplifies it for calculation. for example, a very large number (15 to the power of 56) is ver large to work with if not written in a simplified form.
in exponents when a number is to the power of 1/2 there is a square root sign. for 1/3 there is a cube root sign. is there a sign for numbers like 2/3, 5/6 ..... i dont see it on my calculator.
to me, exponents are a simple, shortened way of expressing a number that is repeatedly being multiplied for a certain number of times. for instance, 3X3X3X3X3X3X3 can simply be written as 3^7... this way is less time consuming and less tediious.
is a quadratic an exponent? wat do u all tink?? i tink it is, since each term in the function is raised to some power. for example.. 2x2 + 2x + 2 = 0. The first x is raised to the power 2, the second x is raised to the power 1 and the number 2 is raised to the power 1...understand??
an exponent is a reptitive number that is concise into smaller way, so you can identify how much repeating number. eg. 2*2*2*2*2*2 that is the reprating number is the base (2) and you have to raised to the power (6) because there are six of the repeating.note that this only appiles to multiplication. but the rule is when u have to multiply two exponent number you add the powers and when you divide you minus the powers. any questions.
another word for 'exponent's indices. the word' indices' came from the root word 'index'. an index is a number or unknown that is appended to a quantity
Laws of Indices There are several rules for dividing and multiplying numbers written in index form. These properties only hold, however, when the same number is being raised to a certain power. For example, we cannot easily work out what 2³×5² is, whereas we can simplify 3²×3³ .
Multiplication When we multiply together index numbers, we add the powers. So: ya × yb = ya+b
Examples x2 × x3 = x5 54 × 5-2 = 52 (because 4 + (-2) = 2) But there is no easy way of calculating 54 × 33 because 5 and 3 aren't the same number!
Division When dividing index numbers, subtract the power of the number we are dividing by from the power of the number being divided. So: ya ÷ yb = ya - b
in real life exponents are very useful in electronics, mechanical and thermodynamic systems. They are also used in biology to determine population growth.
Exponents are a shorter version of multiplication: (6)(6) = 62, (5)(5)(5) = 53. The "exponent" stands for however many times the thing is being multiplied. The thing that's being multiplied is called the "base". This is called "raising to a power", where the exponent is the "power". "53" is "five, raised to the third power". with variables, we need exponents, because its easier to deal with "x6" than with "xxxxxx".
well. the population growth of an area is done exponentially, hmmmm thinking about it so to with the the growth of bacteria and fungi. these are some uses of exponents in real life.
i have read about this term, exponential, and think i can relate it to a real life scenario. it can be used to express the growth of a population and an equation can be deduced from the growth of a population of 250 persons: for if it doubles every year, y= 250 x (2 to the power of x).
Any term raised to the power of 2 is a quadratic, just like any term raised to the power of 1 is linear. using this analogy I would say that a quadratic is an exponent.
Cruiser you recognise an exponent the same way you would recognise any other mathematical operation. eg. +, plus, add, means the same thing but is recognised in different ways. In the operation of exponents ^, exp, or most commonly used is the superscript of the exponent digit are all used to distinguish an exponent.
inorder to understand exponent you need to understand 'base' and 'power'it is the same where a number is multiplied by it self a certain number of times
really what does exponents have to do with quadratic equations when, inorder to solve a quadratic equation you need to use the formula x= -b+_... etc.or by using the difference of squares.
Exponent can be a neat way of writing a very large number for example 10000000000000 is simply 10 to the power 13 or it can be a how much times a number is to be multiplied example 7 to the power of 4 means 7*7*7*7.
i think that an exponent is related to indices eg 3 to the power 5, in this case 3 is the base and 5 is the power so yes ratman it is a number raised to a power and instead of repeating the number by itself your can count the number of times the number is repeated and you can put the number to that power
yes i agree with apocalypse and tweety...it is a simple and easy way to represent large numbers and avoid repetition.. i think it can be considered indices as well.i also think a quadratic is an exponent since there are variables raised to a power. eg. 3x to the power of 3 plus 2x to the power of 2.
Lets pretend that we only know about addition, and not multiplication. Suppose you've heard that multiplication is really hard, and you ask me why it is needed.
Multiplication lets you state problems that would be very big if you just used addition. I can say '5 times 3' where you would have to say '3+3+3+3+3'.
Also multiplication gives us a way to calculate big sums more quickly. To multiply 5*3, I just have to know 1*3=3 and 5*3=15, rather than having to add up 5 3's. So multiplication saves a lot of time.
That's exactly what powers (or exponents) do for you. Just as multiplication (in its simplest form) is just repeated addition, a power is just a repeated multiplication.
Exponents are used as a short way to represent a number. The exponent is the number of times the base is multiplied by itself. and sweediekinks said it perfect
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42 comments:
first up!! what is an exponent?????
is it sumting raised to a power???
or sumting that repeats itslef???
Wake up class
No one is responding to ratsman questions
Exponents are used to represent a number. The exponent is the number of times the base is multiplied by itself.Example 3 TO the power 3 gives you 27
ratman an exponent simply means that you have same number being multiplied a certain number of times. Eg. if u have 2X2X2 .
This can also be 2 to the 3rd power which means you multiply the number (2) three times.
It is what u said. It repeats itself
Exponent is an easier method of writing the product of a reccuring number ie 3x3x3x3x3 in a simpler form of 3 to the power of 5meaning 3 multiply by itself 5 times. If you are implying a quadratic equation,the whole equation is not an exponent only the variable that is raised to a power. For a quadratic, the number is raised to the power of 2. A real life scenario could be a supermarket casher,cashing for a number of items of the same kind with the same price. Instead of punching in the same digits over and over that certain button with an exponent function encoded on the "computerized" cash register is there to use to make her job easier.
exponent simply means that you have a number which is being multiplied by itself a certain number of times.That is the number of times the base number (original number) is being multiplied by itself.
i think the word exponent refers to the power of a number. for example the number 2 to be squared or the number 2 raise to the power of 3. Exponent simply refers to the power.
how do you recognise an exponent. I have never really understood this quite.
how would you do this questio..
y=e -x how yould you work this out ?
Ratman i will try to answer your question to the best of my ability. Firstly an exponent is a mathematical operation. a mathematical operation tells you what particular action to take when the operation is encountered. eg. if we encounter the mathematical operation + we understand to add likewise if encounter the exponent operation we should understand that it means to multiply that number refered to as the base by the exponent (the superscript number)that number of times as stated by the exponent (again the superscript number). your second and third question reffers to the same solution.
cruiser that question does not make much sense to me. can you explain it further?
cruiser if your question is how to work with negative exponents eg 5^-2 (5 raised to the power -2). Simply the solution is 1 divided by 5^2 i.e. 1/25 (i believe). i hope my explaination is accurate as i would not like to post inaccurate information. Could someone please clarify my explaination if necessary.
writing a number in expotent form simplifies it for calculation. for example, a very large number (15 to the power of 56) is ver large to work with if not written in a simplified form.
An exponent is the number of times a base is multiplied by it self.
So yes Ratman the sumthing that is raised to the power is the Base example 10 to the -4th power is = 1/10000
in exponents when a number is to the power of 1/2 there is a square root sign. for 1/3 there is a cube root sign. is there a sign for numbers like 2/3, 5/6 ..... i dont see it on my calculator.
Exponent is a shorter way to show how much times a number is multiplied by itself!!!
example 2 to the 6th power simply means 2x2x2x2x2x2 whereas 6 is the exponent in this example
ratman where the jail you come out from but no cene dog hmm rat i need help to what reelly is exponents
to me, exponents are a simple, shortened way of expressing a number that is repeatedly being multiplied for a certain number of times. for instance, 3X3X3X3X3X3X3 can simply be written as 3^7... this way is less time consuming and less tediious.
is a quadratic an exponent? wat do u all tink?? i tink it is, since each term in the function is raised to some power. for example..
2x2 + 2x + 2 = 0. The first x is raised to the power 2, the second x is raised to the power 1 and the number 2 is raised to the power 1...understand??
an exponent is a reptitive number that is concise into smaller way, so you can identify how much repeating number. eg. 2*2*2*2*2*2 that is the reprating number is the base (2) and you have to raised to the power (6) because there are six of the repeating.note that this only appiles to multiplication. but the rule is when u have to multiply two exponent number you add the powers and when you divide you minus the powers. any questions.
another word for 'exponent's indices. the word' indices' came from the root word 'index'. an index is a number or unknown that is appended to a quantity
Laws of Indices
There are several rules for dividing and multiplying numbers written in index form. These properties only hold, however, when the same number is being raised to a certain power. For example, we cannot easily work out what 2³×5² is, whereas we can simplify 3²×3³ .
Multiplication
When we multiply together index numbers, we add the powers. So:
ya × yb = ya+b
Examples
x2 × x3 = x5
54 × 5-2 = 52 (because 4 + (-2) = 2)
But there is no easy way of calculating 54 × 33 because 5 and 3 aren't the same number!
Division
When dividing index numbers, subtract the power of the number we are dividing by from the power of the number being divided. So:
ya ÷ yb = ya - b
Examples
x2/x3 = x-1
72 ÷ 7-5 = 7-3
Brackets
(ya)b = ya×b
Examples
(x2)3 = x6
(53)2 = 56
exoponents teel us how many times to multiply a number by itself a quatratic exponent is an exponent that contains a quaratic formula e.g 3^x2
in real life exponents are very useful in electronics, mechanical and thermodynamic systems. They are also used in biology to determine population growth.
Exponents are a shorter version of multiplication: (6)(6) = 62, (5)(5)(5) = 53. The "exponent" stands for however many times the thing is being multiplied. The thing that's being multiplied is called the "base". This is called "raising to a power", where the exponent is the "power". "53" is "five, raised to the third power". with variables, we need exponents, because its easier to deal with "x6" than with "xxxxxx".
well. the population growth of an area is done exponentially, hmmmm thinking about it so to with the the growth of bacteria and fungi. these are some uses of exponents in real life.
i have read about this term, exponential, and think i can relate it to a real life scenario. it can be used to express the growth of a population and an equation can be deduced from the growth of a population of 250 persons: for if it doubles every year, y= 250 x (2 to the power of x).
well the use and purpose of the exponent, i think, is a shorthand way to finding the value of a number that has a power.
exponents are use to make numbers into a smaller version for example 10 to the power of 4 is really 10x10x10x10
Any term raised to the power of 2 is a quadratic, just like any term raised to the power of 1 is linear. using this analogy I would say that a quadratic is an exponent.
Cruiser you recognise an exponent the same way you would recognise any other mathematical operation. eg. +, plus, add, means the same thing but is recognised in different ways. In the operation of exponents ^, exp, or most commonly used is the superscript of the exponent digit are all used to distinguish an exponent.
inorder to understand exponent you need to understand 'base' and 'power'it is the same where a number is multiplied by it self a certain number of times
really what does exponents have to do with quadratic equations when, inorder to solve a quadratic equation you need to use the formula x= -b+_... etc.or by using the difference of squares.
so is a number that repeats itslef is the same as raising it to some power?
Exponent can be a neat way of writing a very large number for example 10000000000000 is simply 10 to the power 13 or it can be a how much times a number is to be multiplied example 7 to the power of 4 means 7*7*7*7.
i think that an exponent is related to indices eg 3 to the power 5, in this case 3 is the base and 5 is the power so yes ratman it is a number raised to a power and instead of repeating the number by itself your can count the number of times the number is repeated and you can put the number to that power
yes i agree with apocalypse and tweety...it is a simple and easy way to represent large numbers and avoid repetition.. i think it can be considered indices as well.i also think a quadratic is an exponent since there are variables raised to a power. eg. 3x to the power of 3 plus 2x to the power of 2.
Lets pretend that we only know about addition, and not multiplication. Suppose you've heard that multiplication is really hard, and you ask me why it is needed.
Multiplication lets you state problems that would be very big if you just used addition. I can say '5 times
3' where you would have to say '3+3+3+3+3'.
Also multiplication gives us a way to calculate big sums more quickly. To multiply 5*3, I just have to know 1*3=3 and 5*3=15, rather than having to add up 5 3's. So multiplication saves a lot of time.
That's exactly what powers (or exponents) do for you. Just as multiplication (in its simplest form) is just repeated addition, a power is just a repeated multiplication.
Exponents are used as a short way to represent a number. The exponent is the number of times the base is multiplied by itself.
and sweediekinks said it perfect
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