A power tells how many times the base is used as a factor. The number formed by any power will be the multiple of the given number. The sum of the digits of the product will be equal to the factors of the given number. Before you start solving the problems students must remember that there are some rules to find a product. Know the Procedure on how to raise a number by any power, examples of numbers formed by any power, etc.

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## How to Raise a Number by any Power?

Follow the simple guidelines listed below to obtain Number Formed by any Power. They are as follows

- Firstly, identify the base and power in the given number.
- Later, write down the base as many times as the power and place a multiplication symbol in between them.
- Multiply the numbers and find the result.

### Rules on Numbers Raised by any Powers

1. Any number raised to the power of zero, except zero, equals one.

a^{0 }= 1

2. Any number raised to the power of one equals the number itself.

a¹ = a

3. When bases are equal powers should be added.

### Examples of Number Raised by any Power

**Example 1.**

Write the number 3 formed by any power.

**Solution:
**We have to write the number formed any power for 3.

Let us take random multiples of 3 to check the result.

First multiple any number with 3 and then add the result and check whether it is multiple of 3 like 3, 6, 9.

3¹ = 3 → 3 + 0 = 3 → 3 is a multiple of 3.

3³ = 27 → 2 + 7 = 9 → 9 is a multiple of 3.

3 × 2 = 6 → 6 is a multiple of 3.

3 × 10 = 30 → 3 + 0 = 3 → 3 is a multiple of 3.

3 × 18 = 54 → 5 + 4 = 9 → 9 is a multiple of 3.

3 × 42 = 126 → 1 + 2 + 6 = 9 → 9 is a multiple of 3.

We observe that the number formed by any power is 3, 6, 9.

The sum of the digits of a number formed by 3 will be the multiples of 3.

**Example 2.**

Write the number 9 formed by any power.

**Solution:
**We have to write the number formed any power for 9.

Let us take random multiples of 9 to check the result.

First multiple any number with 9 and then add the result and check whether it is a multiple of 9.

9¹ = 9

9² = 9 × 9 = 81 = 8 + 1 = 9 → 9 is a multiple of 9.

9³ = 9 × 9 × 9 = 729 = 7 + 2 + 9 = 18 = 1 + 8 = 9 → 9 is a multiple of 9.

9

^{4 }= 9 × 9 × 9 × 9 = 6561 = 6 + 5 + 6 + 1 = 18 = 1 + 8 = 9 → 9 is a multiple of 9.

9 × 12 = 108 = 1 + 0 + 8 = 9 → 9 is a multiple of 9.

9 × 428 = 3852 = 3 + 8 + 5 + 2 = 18 = 1 + 8 = 9 → 9 is a multiple of 9.

We observe that the number formed by any power is 9.

The sum of the digits of a number formed by any power for 9 is 9.

**Example 3.**

Write the number 5 formed by any power.

**Solution:**

We have to write the number formed any power for 5.

Let us take random multiples of 5 to check the result.

Multiply the numbers with any power and then check whether it is a multiple of 5.

We know that the multiplies of 5 will have 0 or 5 in its last digit.

5¹ = 5 → 5 is a multiple of 5.

5² = 5 × 5 = 25 → 5 is a multiple of 5.

5³ = 5 × 5 × 5 = 125 → 5 is a multiple of 5.

5^{6 }= 5 × 5 × 5 × 5 × 5 × 5 = 15625 → 5 is a multiple of 5.

All the values above are having 5 in their last digit which means the above numbers are multiples of 5.

**Example 4.**

Write the number 2 formed by any power.

**Solution:**

We have to write the number formed any power for 2.

Let us take random multiples of 2 to check the result.

Multiply the numbers with any power and then check whether it is a multiple of 2.

We know that the multiplies of 2 will have 0, 2, 4, 6, 8 at its last digit.

2¹ = 2 → 2 is a multiple of 2.

2² = 2 × 2 = 4 → 4 is a multiple of 2.

2³ = 2 × 2 × 2 = 8 → 8 is a multiple of 2.

2 × 126 = 252 = 252 is a multiple of 2.

All the values above are having 2, 4, 8 in their last digit which means the above numbers are multiples of 2.

**Example 5. **Write the number 6 formed by any power.

**Solution:**

We have to write the number formed any power for 6.

Multiply the numbers with any power and then check whether it is a multiple of 5.

Let us take random multiples of 6 to check the result.

6 × 50 = 300 = 3 + 0 + 0 = 3

6 × 23 = 138 = 1 + 3 + 8 = 12 = 1 + 2 = 3

6 × 68 = 408 = 4 + 8 = 12 = 1 + 2 = 3

6² = 6 × 6 = 36 = 3 + 6 = 9

6³ = 6 × 6 × 6 = 216 = 2 + 1 + 6 = 9

We observe that the number formed by any power is 3, 9.

The sum of the digits of a number formed by 6 will be the multiples of 3.