The addition of two exponents can be done quickly with this online adding exponents calculator. Additionally, you can also add numbers with negative exponents.

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## What is an Exponent?

It is easier to express a number or an expression in exponent form when it is multiplied by itself numerous times. 125, for example, is written as 53 and equals (5 * 5 * 5).

The exponent form of (5 * 5 * 5) is called 53, and its value is 125. When 53 replaces 125, we say the base is 5 and the exponent is 3. Exponent is also known as index. Indices is the plural form of index.

The number of times the base is multiplied by itself is the power. In Example 53, we state that 125 is the third power of 5, or that 125 is 5 to the power of 3 (53).

## How to Use Adding Exponents Calculator?

• Enter the exponents and base values in the appropriate fields to add the exponents in the above calculator.
• The calculator will instantly add both exponents.

## How to Add Two Exponents ?

Exponent addition is very similar to the addition of integers. Exponents must first be simplified before being added, and the values we obtain after the simplification are then added. We have answered a few examples below that should put all of your questions about the addition of exponents to rest.

### Case 1 : Different Base & Exponents

Example

1. Add exponents : 56 + 43

Solution :

First exponent : 56 = 5 x 5 x 5 x 5 x 5 x 5 = 15625. (multiplying the base value{5}, number of times of exponent value {6})

Second exponent : 43 = 4 x 4 x 4 = 64. (multiplying the base value {4}, number of times of exponent value {3})

We have simplified both the exponents, now just add the values.

= 56 + 43
= (5 x 5 x 5 x 5 x 5 x 5) + (4 x 4 x 4)
= 15625 + 64
= 15689.

The addition of exponents 56 + 43 = 15689.

Example

2. Add exponents : 26 + 62

Solution :

We’ll follow the same procedure as in the previous example.

= 26 + 62
= (2 x 2 x 2 x 2 x 2 x 2) + (6 x 6)
= 64 + 36
= 100

The addition of exponents 26 + 62 = 100.

### Case 2 : Same Base & Exponents

Example

3. Add exponents : 53 + 53

Solution :

When the base and exponents are same you can use the same above process to solve the problem, but her in this case as the both exponents are similar you can just simplify any one exponent and multiply it with 2. This can save your time.

First Exponent = 53 = 5 x 5 x 5 = 125

= 53 + 53
= 2 (53)
= 2 (125)
= 250

The addition of exponents 53 + 53 = 250.

Example

4. Add exponents : 24 + 24

Solution :

First Exponent = 24 = 2 x 2 x 2 x 2 = 16

= 24 + 24
= 2 (24)
= 2 (16)
= 32

The addition of exponents 24 + 24 = 32.

### Case 3 : Negative Exponents

Example

5. Add exponents : 2-3 + 5-4

Solution :

The exponents in this case are negative (-). The approach of addressing the problem is the same as it was in case 1 even if the exponents signs are negative since the base and exponents values differ.

But before moving on, be aware that the method of simplification could change slightly. As the exponents have a negative sign, we must first change it to a positive sign (+) in order to move forward. A step-by-step process for performing the addition of negative exponents is shown below.

First Exponent = 2-3, We must divide the entire term by 1 in order to make this exponent positive.

First Exponent = 2-3 = 1/23, Once we have changed the exponent’s value to positive, simply simplify as usual.

First Exponent = 2-3 = 1/23 = 1/ (2 x 2 x 2) = 1/ 8 = 0.125

Second Exponent = 5-4 = 1/54 = 1/ (5 x 5 x 5 x 5) = 1/ 625 = 0.0016

= 2-3 + 5-4
= 1/23 + 1/54
= 0.125 + 0.0016
= 0.1266

The addition of exponents 2-3 + 5-4 = 0.1266

Example

6. Add exponents : 6-4 + 9-2

Solution :

Convert the exponents into positive form by dividing it by 1 and simplify.

= 6-4 + 9-2
= 1/64 + 1/92
= [1/(6 x 6 x 6 x 6)] + [1/(9 x 9)]
= (1/1296) + (1/81)
= 0.0008 + 0.0123457
= 0.0131457

The addition of exponents 6-4 + 9-2 = 0.0131457