Question

3
Use one of the exponent rules to simplify the following expression:



A
16926169^{26}169
26


B
262626^{26}26
26


C
132613^{26}13
26


D
131213^{12}13
12

Answer 1

To simplify the given expressions using exponent rules, we can recall some basic properties of exponents. One useful property is:

\[
a^{m \cdot n} = (a^m)^n
\]

Now, let's analyze the expressions one by one:

### A: \( 16926169^{26} \)

This expression can be interpreted as \( (1692 \cdot 169)^{26} \).
However, since it is a single number raised to a power, we simply consider it as \( 16926169^{26} \).
If there's no further simplification possible due to lack of factors, we leave it as is:

\[
16926169^{26}
\]

### B: \( 262626^{26} \)

Similar to the first one, this can be interpreted as \( (2626 \cdot 26)^{26} \).
But again, there’s no simplification since it’s just a number raised to the power.

\[
262626^{26}
\]

### C: \( 132613^{26} \)

Following the same logic, this could be interpreted as \( (1326 \cdot 13)^{26} \), but we have no further factorization to do.

\[
132613^{26}
\]

### D: \( 131213^{12} \)

This, too, is just a number raised to a power:

\[
131213^{12}
\]

### Summary
If we look for specific simplification based on exponent rules for each of these expressions, they simply remain in their original states since there’s no shared bases or appropriate factorization provided.

Thus, the results after simplification are:
- A: \( 16926169^{26} \)
- B: \( 262626^{26} \)
- C: \( 132613^{26} \)
- D: \( 131213^{12} \)

None can be reduced further without additional context or factoring.