## Definition of exponent

An Exponent is a number that states how many times the base number is to be used in multiplication. The Exponent Number appears on the top right of the base number as a small number.

### Basic exponent rules

- 5
^{5}means 5×5. The smaller number 2 is the Exponent and denotes the number of times 5 needs to be multiplied. - So instead of writing 2x2x2 we can simply write 2
^{3} - The Exponent way is much shorter and easier to write a
^{n}and comes in handy when you need to solve big equations. Exponents are also known as Index or Power. - Thus we can say that tells you to multiply ‘a’ by itself ‘n’ number of times.

**Example:** 3^{5} = 3x3x3x3x3= 243

## Properties of exponents

### Suppose A = 1 or 0 exponent

- If the Exponent is 1 then you have the number itself. Example: = 9
^{1}= 9 - If the Exponent is 0 then you get 1. Example: 5
^{0}= 1 - If both the Number and the Exponent is zero 0
^{0}then the result is indeterminate.

### Negative Exponents

A Negative Exponent is just the opposite of Multiplication, that is Division.

So, 5^{-1}

Is basically 1/5^{2} = 1/25= 0.04

A negative exponent means how many times you need to divide 1 by the number.

**Example:** 6^{-3} = 1/= 0.0046

### Grouping exponents with signs

In order to avoid confusions, use Parenthesis like () brackets.

**There is a difference:**

- With brackets: (ab)
^{2}= (ab)x(ab) - Without brackets: ab
^{2}= axbxb

**Example:**

- -2
^{2}= (-2)X(-2)= 4 - -2
^{2}= -(2)^{2}= -4

### Special exponents:

- When a number has an Exponent of 2, it is called Squared.
- When a number has an Exponent of 3, it is called Cubed.

### Special cases:

**Example :** 5^{2} x 5^{3}

- Is same as 5 to the power of 2+3 or 5
^{2} - So when the bases are same you can add the exponents during Multiplication.

**Example:**

- This is the same as 3 to the power of 4×2 or 3
^{2} - This is the case of exponent on top of an Exponent and here we multiply the Exponents.

## Worksheet on exponents

**1. Write the expression using exponents:**

**a)** 56 x 56 x 56

**b)** 1.8×1.8×1.8×1.8×1.8×1.8

**c)** (-2)x(-2)x(-2)x(-2)

**Ans:** 56^{3}; 1.8^{3}; -2^{4}

**2. Solve the following exponents:**

**a)** 10^{3}

**b)** 0^{4}

**c)** 2^{6}

**d)** 1^{8}

**Ans:** 1000; 0; 64; 1

**3. Solve the following equations:**

**a) **-(1/2)^{5}

**b) **-0.5^{2}

**c) **-1.2^{3}

**d) **-(5/2)^{3}

**Ans:** 1/32; 0.25; 1.2; 125/8

**4. Solve the equations:**

**a) **10^{-3}

**b) **3^{-2}

**c) **5^{-4}

**d) **1^{-1}

**Ans:** 1/1000; 1/9; 1/625; 1