How to add exponents with the same base and different power?

To add expressions with exponents that share the same base but have different powers, you can't directly add the exponents. Instead, you must evaluate each term separately and then add the results.

Steps to Follow:

1. Check the bases and exponents: According to the provided references, the first step is to check that the terms you are trying to add have the same base but different exponents.

2. Evaluate each term: Calculate the value of each exponential term individually. This means calculating the base raised to its respective power.

3. Add the results: Sum the values you obtained in the previous step. This gives you the final answer.

Examples:

Here's a breakdown with examples:

Example 1:

Calculate 2² + 2³

Step	Description	Calculation
1	Bases are the same (2), exponents are different (2 and 3).	N/A
2	Calculate 22	22 = 4
3	Calculate 23	23 = 8
4	Add the results	4 + 8 = 12
Answer		12

Example 2:

Calculate 3¹ + 3² + 3⁰

Step	Description	Calculation
1	Bases are the same (3), exponents are different (1, 2, and 0).	N/A
2	Calculate 31	31 = 3
3	Calculate 32	32 = 9
4	Calculate 30	30 = 1
5	Add the results	3 + 9 + 1 = 13
Answer		13

Important Note: You cannot simplify expressions like 2² + 2³ to 2⁵. The rule a^m aⁿ = a^m+n applies to multiplication*, not addition.