2 exposant 4 + 2 exposant 6
How to simplify it with the base and the exposant

Given the expression:

\[
2^4 + 2^6
\]

### Step-by-Step Simplification

1. **Identify the common base**: Both terms have the base \(2\).

2. **Factor out the smallest power**: The smallest exponent is \(4\), so we can factor \(2^4\) out of the expression:

   \[
   2^4 + 2^6 = 2^4(1 + 2^{2})
   \]

3. **Simplify inside the parentheses**: \(2^2 = 4\), so:

   \[
   2^4(1 + 4) = 2^4 \times 5
   \]

4. **Final simplified expression**: The expression \(2^4 \times 5\) is the simplified form, with a common base of \(2\) and an exponent of \(4\).

### Final Answer

\[
2^4 + 2^6 = 2^4 \times 5
\]

Would you like further details or have any other questions?

### Related Questions

1. How would you simplify \(3^5 + 3^7\) using the same method?
2. What is the result of \(2^4 \times 5\) in numerical form?
3. How can you express \(2^4 \times 5\) as a single exponentiation?
4. How would you factor \(5^3 + 5^5\) using a similar approach?
5. Can the expression \(a^m + a^n\) always be factored like this?

### Tip

When simplifying expressions with exponents, look for the smallest exponent to factor out a common base!

2 exposant 4 + 2 exposant 6: How to simplify it with the base and the exposant?

Learn how to simplify the expression 2^4 + 2^6 by factoring out the smallest exponent. This problem involves exponent rules and factoring techniques, suitable for students in Grades 8-10.

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