## What Is Index Form?

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## What is index form with example?

What is index notation? – Index notation is a way of representing numbers (constants) and variables (e.g. x and y ) that have been multiplied by themselves a number of times. Below are all examples of expressions involving index notations: \ We use index notations, or the plural ‘indices’, to simplify expressions or solve equations involving powers.E.g.

Simplify 6 × 6 × 6 × 6 6 is being multiplied by itself 4 times. We can therefore write this as 6 4 This is said as ” 6 to the power of 4 ” E.g Simplify x × x × x × x x is being multiplied by itself 4 times. We can therefore write this as x 4 This is said as “x to the power of 4 ” E.g Simplify 2y × 2y × 2y × 2y In this question the term 2y is being multiplied by itself 4 times.

Therefore you can write this as 2y 4 This is said as “2y to the power of 4 ”

### What is 2x2x2x2 in index form?

Laws of indices – Indices are the small numbers in the top right corner of a number and raise your base to a power, e.g.2 4 = 16 because it means 2x2x2x2. You should be familiar with the powers and roots of number up to 15 2 and 5 3, When dealing with indices, there are some shortcuts that you should be familiar with when making calculations and these are used not only for numbers, but also when dealing with letters. However, the shortcuts will only work if you have the same base!

## What is the index form of 25?

We know that: 5 5 = 25 The product 5 5 can be written as 5 2, 5 5 is known as the expanded form (or factor form ) of 25 and 5 2 is known as the index form of 25. Generally when a number is multiplied by itself any number of times, the expression is simplified by using the index notation.#### What is the index form of 400?

Ans : 2^4 × 5^2. Explanation : 400 = 2×2×2×2×5×5.400 = 2^4 × 5^2.

### What is the index form of 300?

is a way of writing very large and very small numbers so that they are easier to understand and work with. It is also called standard index form or scientific notation, Any number in standard form is written as:

- A × 10ⁿ
- A is a number that is equal to or greater than 1 and less than 10, n is the to multiply by to get the original value.
- For example, 300 in standard form would be 3 x 10². A = 3 and n = 2
- The integer power of ten is positive for numbers greater than 10 and negative for values less than 1. For numbers that are between 1 and 10, the integer power of ten is zero.
- It is useful to have a good understanding of place value as well as multiplying and dividing by powers of ten,

Standard index form is used in computer game design. Watch the video to listen to games developer Shahan describe how he uses standard index form in his work. Bobby : Hi, Shahan. Shahan : Hi, Bobby. Bobby : You’re a games developer, right? Shahan : I am indeed, so I’m a programmer which means I use computer language and maths to develop games.

Bobby : So, tell me about a game you’ve been working on recently. Shahan : So, recently I’ve been making a game called Stellar, where you travel across space to fight aliens using nanotechnology. Bobby : Nanotechnology, that’s really small, right? Shahan : Really, really small and in fact, if I was to write it down by hand, it would take me absolutely ages.

The same with typing out, so what we do for our nanotechnology is define it as eight times ten to the power of minus nine. Bobby : That’s standard index form! So, mathematically, it would be the decimal point followed by eight zeros, then the number. Shahan : Exactly, and we also use it to write out really huge numbers as well.

For example, in our game, we’ve set our alien planet as three times ten to the power of fifteen kilometres away from Earth. So that’s another standard index form to make it a lot simpler for us. Bobby : So, where else might you see maths turn up in your work? Shahan : Absolutely everywhere. I mean, there’s all sorts of maths all across game development.

Algebra, for example, is fundamental when it comes to coding. Lots of languages use algebra to substitute in big numbers, small numbers for letters and that just makes our lives a lot easier. Bobby : So I can see now how standard index form and, indeed, maths can make your life simpler as a games developer.

### How do you write 144 in index form?

Step 1/2 First, we find the prime factors of 144.144 can be divided by 2, the smallest prime number: 144 ÷ 2 = 72 72 can also be divided by 2: 72 ÷ 2 = 36 36 can also be divided by 2: 36 ÷ 2 = 18 18 can also be divided by 2: 18 ÷ 2 = 9 Now, 9 can be divided by 3, another prime number: 9 ÷ 3 = 3 Step 2/2 Finally, 3 is a prime number itself.

### How do you write 64 in index form?

Answer: 4³ is the index form of 64 Step-by-step explanation: 64 is a basic numeral or number.4³ is the index form (or power form) of 64.4 × 4 × 4 is the expanded form of 64. For 64 = 4 × 4 × 4 = 4³, the base number 4 appears three times as a factor of the basic numeral (or number) 64.

### What is the index form of 1000?

For example, the number ‘100’ can be represented as ’10 x 10′ – that is, 102. ‘1000’ is ‘ 10 x 10 x 10 ‘, or 103. What do you notice about the pattern between the written number and its representation in index notation form? it is represented in index form as 108.

#### What is the index form of 432?

432 as a Power of 10 – As outlined above, there is more than one way to write 432 as a power of 10, Like any number written in scientific notation, 432 has a significand (sometimes called a mantissa or coefficient) of 4.32 multiplied by the power of ten 100 expressed by the base 10 and index 2: 432 = 4.32 x 100 = 4.32 × 10 2,

Writing a number as a power of 10 is a “shorthand” form to express a repeated multiplication, too. By the way: There are two conventions for naming powers of ten, known as the long and the short scale. In English, the short scale is used almost everywhere these days, including on this website. En passant: Sites which are related to scientific notation, exponents or numbers can be found in the “recommended sites section” in our sidebar.

In the section ahead, we are going to shed a light on the frequently asked questions in the context. You may be surprised to learn what other people like to know.

## What is the index form of 40?

This can be written in index form as 2 3 × 5. This answer can be checked by making sure 2 × 2 × 2 × 5 is equal to 40.2 × 2 × 2 × 5 = 40, so this answer is correct.

#### What is the index form of 4200?

Answer: 4200 in scientific notation = 4.2 × 103. Our tool changes any decimal number including 4200 to standard index form.

### What is the index form of 36?

First write down any two factors of 36 (numbers that multiply together to give 36). Let’s use 2 x 18. We now need to break these numbers down into prime factors.2 is already a prime number, so we only need to break down 18. We do for 18 what we did for 36: choose two numbers that multiply to give 18.

### What is the index form of 1260?

1260 as a Power of 10 – As outlined above, there is more than one way to write 1260 as a power of 10, Like any number written in scientific notation, 1260 has a significand (sometimes called a mantissa or coefficient) of 1.26 multiplied by the power of ten 1000 expressed by the base 10 and index 3: 1260 = 1.26 x 1000 = 1.26 × 10 3,

- Writing a number as a power of 10 is a “shorthand” form to express a repeated multiplication, too.
- By the way: There are two conventions for naming powers of ten, known as the long and the short scale.
- In English, the short scale is used almost everywhere these days, including on this website.
- En passant: Sites which are related to scientific notation, exponents or numbers can be found in the “recommended sites section” in our sidebar.

In the section ahead, we are going to shed a light on the frequently asked questions in the context. You may be surprised to learn what other people like to know.

#### What is the index form of 150?

150 as a Power of 10 – As outlined above, there is more than one way to write 150 as a power of 10, Like any number written in scientific notation, 150 has a significand (sometimes called a mantissa or coefficient) of 1.5 multiplied by the power of ten 100 expressed by the base 10 and index 2: 150 = 1.5 x 100 = 1.5 × 10 2,

Writing a number as a power of 10 is a “shorthand” form to express a repeated multiplication, too. By the way: There are two conventions for naming powers of ten, known as the long and the short scale. In English, the short scale is used almost everywhere these days, including on this website. En passant: Sites which are related to scientific notation, exponents or numbers can be found in the “recommended sites section” in our sidebar.

In the section ahead, we are going to shed a light on the frequently asked questions in the context. You may be surprised to learn what other people like to know.

#### How do you write 343 in index form?

Answer and Explanation: The index form of 343 is 7^3 or 7 x 7 x 7. The ‘index form’ of a number shows the number as the product of its prime factors. The factors of 343 are 1, 7, 49, and 343.

## What is the index form of 1800?

1800 as a Power of 10 – As outlined above, there is more than one way to write 1800 as a power of 10, Like any number written in scientific notation, 1800 has a significand (sometimes called a mantissa or coefficient) of 1.8 multiplied by the power of ten 1000 expressed by the base 10 and index 3: 1800 = 1.8 x 1000 = 1.8 × 10 3,

- Writing a number as a power of 10 is a “shorthand” form to express a repeated multiplication, too.
- By the way: There are two conventions for naming powers of ten, known as the long and the short scale.
- In English, the short scale is used almost everywhere these days, including on this website.
- En passant: Sites which are related to scientific notation, exponents or numbers can be found in the “recommended sites section” in our sidebar.

#### What is the index form of 240?

Step-by-step explanation: The orange divisor(s) above are the prime factors of the number 240. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 5 = 240. It can also be written in exponential form as 2⁴ x 3¹ x 5¹.

#### What is the index form of 500?

500 as a Power of 10 – As outlined above, there is more than one way to write 500 as a power of 10, Like any number written in scientific notation, 500 has a significand (sometimes called a mantissa or coefficient) of 5 multiplied by the power of ten 100 expressed by the base 10 and index 2: 500 = 5 x 100 = 5 × 10 2,

Writing a number as a power of 10 is a “shorthand” form to express a repeated multiplication, too. By the way: There are two conventions for naming powers of ten, known as the long and the short scale. In English, the short scale is used almost everywhere these days, including on this website. En passant: Sites which are related to scientific notation, exponents or numbers can be found in the “recommended sites section” in our sidebar.

### What is the index form of 1600?

Therefore: 1600 = 1.6 × 10 3. This can also be expressed as 1.6 × 10^3, using the caret symbol, or as 1.6e+3, which is called 1600 in e-notation, further discussed in the section ahead.

### How do you write 32 in index form?

Hence ’32’ can be written as 2 × 2 × 2 × 2 × 2 which is in the form of the product of prime numbers.2⁵ is the index notation of 32 where ‘2’ is base and ‘5’ is power or exponent.

### What is the index form of 1000?

For example, the number ‘100’ can be represented as ’10 x 10′ – that is, 102. ‘1000’ is ‘ 10 x 10 x 10 ‘, or 103. What do you notice about the pattern between the written number and its representation in index notation form? it is represented in index form as 108.

#### How do you write 32 in index form?

Hence ’32’ can be written as 2 × 2 × 2 × 2 × 2 which is in the form of the product of prime numbers.2⁵ is the index notation of 32 where ‘2’ is base and ‘5’ is power or exponent.

#### What is the index form of 36?

First write down any two factors of 36 (numbers that multiply together to give 36). Let’s use 2 x 18. We now need to break these numbers down into prime factors.2 is already a prime number, so we only need to break down 18. We do for 18 what we did for 36: choose two numbers that multiply to give 18.