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In maths, there are various ways of writing the same thing. For example, we could say 5 equals 4 + 1, or 3 +2 or even 10 - 5.
5 = 4 + 15 = 3 + 25 = 10 -5
Essentially, we have just written the number 5 in a different way.
When we multiply a number with itself, lets say we represent that number using the letter a, we can write this as a x a.
Lets say a = 5,
so 5 x 5 = 25.
Another way of writing 5 x 5 is by using index form. We can rewrite 5 x 5 as 52.
If it were 5 x 5 x 5 x 5, we can write this as 54.
Imagine in an exam, during school or anywhere else writing5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5.
This would take a large amount of your time and you can easily make a mistake. For example, you might write an extra 5 by mistake. So by writing in index form, it is much easier just to write 59.
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 59
So any number can be written in index form.
If we wanted to write 1/2 x 1/2 x 1/2 in index form, it would be(1/2)2.
What if the power was negative?
What if the question was to find what 5-1 equals. When we have a negative power, we write 5-1 as 1/(51).
5-1 = 1/(51)
Lets say we have a-n, then we would write this as 1/(an). Some examples are below.
e.g. 64-4 = 1/( 644) a = 67, n = 4 2-10 = 1/( 210) a = 2, n = 10 10-3 = 1/(103) a = 10, n = 3
SO NOW WE KNOW HOW TO WRITE IN INDEX FORM AND WHAT IT MEANS.
5 = 4 + 15 = 3 + 25 = 10 -5
Essentially, we have just written the number 5 in a different way.
When we multiply a number with itself, lets say we represent that number using the letter a, we can write this as a x a.
Lets say a = 5,
so 5 x 5 = 25.
Another way of writing 5 x 5 is by using index form. We can rewrite 5 x 5 as 52.
If it were 5 x 5 x 5 x 5, we can write this as 54.
Imagine in an exam, during school or anywhere else writing5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5.
This would take a large amount of your time and you can easily make a mistake. For example, you might write an extra 5 by mistake. So by writing in index form, it is much easier just to write 59.
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 59
So any number can be written in index form.
If we wanted to write 1/2 x 1/2 x 1/2 in index form, it would be(1/2)2.
What if the power was negative?
What if the question was to find what 5-1 equals. When we have a negative power, we write 5-1 as 1/(51).
5-1 = 1/(51)
Lets say we have a-n, then we would write this as 1/(an). Some examples are below.
e.g. 64-4 = 1/( 644) a = 67, n = 4 2-10 = 1/( 210) a = 2, n = 10 10-3 = 1/(103) a = 10, n = 3
SO NOW WE KNOW HOW TO WRITE IN INDEX FORM AND WHAT IT MEANS.
Video 1
Video 1
What if the power was a fraction? Check out video 1. IT IS NOT HARD.
A fraction has two components. The number on top is called the numerator and the bottom number is called the denominator.
Lets say we have ax/y, where a is a number and x/y is a fraction. Then ax/y would equal the yth root of a to the power of x. You might not understand this at first. KEEP READING IT IS NOT HARD.
Lets say you have 51/2. The power is a 1/2. This is a fraction where 1 is the numerator and 2 is the denominator. To find what 51/2 equals, you would first take the second root of five (square root of 5). The square root of 5 is then put to the power of the numerator which is 1. So the answer is square root of 5 as shown below.
51/2 = (√5)1 = √5 = 2.24 (to 2 decimal places)
If we want to know what 52/3 equals, first look values of the denominator and numerator.
We would first take the third root of 5, then the third root of 5 is put to the power of the numerator which is 2, as shown below.
52/3 = (∛5)2 = 2.92 (to 2 decimal places)
What if the power was a negative fraction? Check out the second video. IT IS NOT HARD.
Do the same thing as though the fraction was not negative (AS EXPLAINED ABOVE). Whatever answer you get, put it over 1 as shown in the video.
A fraction has two components. The number on top is called the numerator and the bottom number is called the denominator.
Lets say we have ax/y, where a is a number and x/y is a fraction. Then ax/y would equal the yth root of a to the power of x. You might not understand this at first. KEEP READING IT IS NOT HARD.
Lets say you have 51/2. The power is a 1/2. This is a fraction where 1 is the numerator and 2 is the denominator. To find what 51/2 equals, you would first take the second root of five (square root of 5). The square root of 5 is then put to the power of the numerator which is 1. So the answer is square root of 5 as shown below.
51/2 = (√5)1 = √5 = 2.24 (to 2 decimal places)
If we want to know what 52/3 equals, first look values of the denominator and numerator.
We would first take the third root of 5, then the third root of 5 is put to the power of the numerator which is 2, as shown below.
52/3 = (∛5)2 = 2.92 (to 2 decimal places)
What if the power was a negative fraction? Check out the second video. IT IS NOT HARD.
Do the same thing as though the fraction was not negative (AS EXPLAINED ABOVE). Whatever answer you get, put it over 1 as shown in the video.
Video 2 (Coming Soon)
Video 2 (Coming Soon)
What if the power was a negative fraction? Check out the second video. IT IS NOT HARD.
Do the same thing as though the fraction was not negative (AS EXPLAINED ABOVE). Whatever answer you get, put it over 1 as shown in the video.
Do the same thing as though the fraction was not negative (AS EXPLAINED ABOVE). Whatever answer you get, put it over 1 as shown in the video.
Try these questions.
Write the 3 x 3 x 3 x 3 x 3 x 3 in index form?
Write 1/4 x 1/4 x 1/4 x 1/4 in index form?
Does 64 equal 6 x 6 x 6 OR 6 x 6 x 6 x 6?
Answers:
36
(1/4)4
64 = 6 x 6 x 6 x 6
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