The **exponents** of a number says **how many times **to use the number in a multiplication.

5³ = 5 x 5 x 5

In words 5³ could be called as 5 to the power 3 or 5 cube**.**

**Question 1 : **

Express m x m x n x n in exponential form.

**Solution :**

Here m is repeating 2 times. To write m x m in the exponential form, we have to write it as m².

Like that n is also repeating 2 times. To write n x n in the exponential form, we have to write it as n²

Hence, the exponential form of m x m x n x n = m² x n²

**Question 2 :**

Express 5 x 5 x 5 in exponential form.

**Solution :**

Here 5 is repeating 3 times. To write 5 x 5 x 5 in the exponential form we have to write it as 5³

**Rule 1 :**

Whenever we want to simplify two or more terms which are having the same base, then we have put only one base and add the powers.

**Rule 2 :**

Whenever we want to simplify the terms which are dividing with the same base, we have to put only one base and subtract the powers.

**Rule 3 :**

Whenever we have power to the power, we have to multiply both powers.

**Rule 4 :**

Anything to the power zero is 1.

**Rule 5 :**

If we have same power for 2 or more terms which are multiplying or dividing then we have to distribute the power for those terms which are multiplying or dividing inside the bracket.

Note :

This rule is not applicable if two or more terms which are adding and subtracting.

For example (x + y) ^m = (x^m + y^m) is not correct

that is x = 4² |
If the power goes from one side of equal sign to the other side, it will flip. |

The other names of exponent are index and power.

Other things:

Point 1:

If we don't have any number in the power then we have to consider that there is 1

Point 2:

In case we have negative power for any fraction and if we want to make it as positive, we can write the power as positive and we should write its reciprocal only. For example

**Question 3 :**

Simplify 4 x ^(-1)/x^(-1/3)

**Solution :**

Find the value of 2(256) ^(-1/8)
= 2 (2^8)^(-1/8) = 2 (2^-1) = 2/2 = 1 |

**Question 5 :**

Find the value of

**Question 6 :**

Find the value of x^(a - b) x^(b - c) x^(c - a)

**Solution :**

**Question 7 :**

Find the value of (8/27)^(-1/3) (32/243)^(-1/5)

**Solution :**

You can try these problems based on laws of exponents.

1. Express 7 x 7 x 5 x 5 in exponential form.

2. Express 13 x b x b x b x b in exponential form.

3. Express 17 x 17 x w x w x w in exponential form.

4. Express 5 x 5 x p x p x p in exponential form.

5. Express n x n x n x b x b in exponential form.

6. Express 9 x 9 x 9 x c in exponential form.

7. Express 4 x 4 x 4 x k x k in exponential form.

8. Express 2 x 2 x 2 x r x r in exponential form.

- Generating equivalent numerical expressions
- Use repeated multiplication
- Division facts
- Exponents
- Using exponents
- Finding the value of a power
- Finding the value of each power
- Find the missing exponent
- Find the missing base
- Finding the factors of a number
- Finding the prime factorization of a number
- using ladder diagram for prime factorization
- Order of operations
- Exploring the order of operations
- Evaluating the numerical expression
- Using exponents with parentheses

After having gone through the stuff given above, we hope that the students would have understood "Exponents".

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