# Introduction to Indices | Additional Mathematics

Learning focus in this video. We are going to discuss what is indexes indexed number. So what is indexed number and index number is the number which is raised to a power and the power also known as the index tells you how many times you have to multiply the number by yourself!

So what does this means? let’s go to the next, like first positive, integral indexes when the real number a is multiplied by itself and times. The results is the n power of a for examples? We have a number 8 here in multiplied by itself or 5 times a times a times a times a times a!

We write this as a with superscript 5, and we call this a to the power of 5 or the 5th power of a, and this number is an indexed number, a number raised to certain power. If the power is 5 means that this number multiplied by itself for 5 times.

Let’s see another example: 7 multiplied by itself for 4 times, then it become 7 to the power of 4, and we say this is the fourth power of 7 and the last one’s 13th multiplied by itself for three times, and this is the third power of 13 n, or we call this 13 to the power of 3! So for an index numbers, we write a number with a superscript of another number and the superscript is called the index or the component, and this number is called the base! Let’s see this example express in index form and find the values of the following! Let’s start with a ok, we have a number 8 multiplied by itself for six times by one two, three, four, five, six, so a okay, so they would like us! The question would like us to express it in index form so in index form!

We write this as 8 to the power of 6! Okay, i’ve created a little table for these calculations from here we can see that if we multiply this number eight four six times is equal to 260 mm 144. So let’s write this down. 262 144 for b, we are asked to find zero point, 3 multiplied by itself or four times in index form! We write this as zero point three to the power of four okay, and this is equal to okay, again um. You can do this by using your calculators?

Okay, i have done this by using microsoft excel okay. So we can see that when zero point, 3 multiplied by itself or four times is equal to zero point: zero, zero, eight one okay. So this is zero point: zero, zero, eight one! now, let’s move on to see yeah okay, so we have negative 5 multiplied by itself or five times, and therefore the index numbers is negative. Five brackets 5, okay, no take notes that we must include the brackets into the practice when we put an index numbers. Okay!

Now, let’s see what’s difference between the index for a negative number with brackets and without brackets for examples, negative 5, squared and brackets negative 5 square? Okay.

Now for this one, only the five will multiply by itself for two times: okay, but not the negative? So it will become something like this as negative and then five times, five! Okay- and this is equal to negative twenty five, and for this one buff, the negative and five will multiply by itself or two times and therefore this will become positive, 25!

Okay, so therefore the index number for negative numbers?

We must include the brackets okay and by using the calculators, you should able to get negative three one, two, five okay.

So this is how we find the values of an index number and how we write a number in index. Number? Let’s proceed to next questions find the values of the following: the first one 3 to the power of 5, so 3 to the power of 5 is equal to 3 times 3 times 3 times, 3 times, 3, okay, so 3 times, 3, 9, okay! this is for this one and 3 times, 3 9, so we have another 9 and then times 3, okay and 9 times. 9 is 81 times 3 and this is equal to 243.

So this is the answer and for b zero point 3 to the power of 3 b, zero point 3 to the power of sorry 0. 2 0.

2 to the power of three equal to 0. 2 times 0. 2 times, 0. 2, okay, 2 times 2, 4, 4 4 times 2, 8 8 and then so we have three decimal places. So in total we need to have three decimal places and 0! 008. So this is answer c1 over 6 to the power of 4 is equal to 1 over 6 times 1 over 6 times 1 over 6 times 1 over 6. Ok, by using your calculators, you should get 1 over 1 2, 9 6 and for the last one, the negative 7 to the power of 5 equal to negative 7 times. Let’s put the brackets and negative 7 times negative 7 times negative 7 times negative 7 and neither 7! So by using your calculators, you should get the answer: negative 1, 6 8 0 7. So this is the answer. Ok, so that’s how we find the value of an index number you? .