Question

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 expressions using exponent rules, we need to look closely at each option. The general exponent rules we'll use include:

1. \( a^m \times a^n = a^{m+n} \)
2. \( (a^m)^n = a^{m \times n} \)
3. \( a^0 = 1 \) (for \( a \neq 0 \))

Now, let's evaluate each option:

**Option A: \( 169^{26} \times 169^{26} \)**

Using the first exponent rule:
\[
169^{26} \times 169^{26} = 169^{26 + 26} = 169^{52}
\]

**Option B: \( 26^{26} \times 26^{26} \)**

Using the first exponent rule:
\[
26^{26} \times 26^{26} = 26^{26 + 26} = 26^{52}
\]

**Option C: \( 13^{26} \times 13^{26} \)**

Using the first exponent rule:
\[
13^{26} \times 13^{26} = 13^{26 + 26} = 13^{52}
\]

**Option D: \( 13^{12} \times 13^{12} \)**

Using the first exponent rule:
\[
13^{12} \times 13^{12} = 13^{12 + 12} = 13^{24}
\]

So, let's summarize the simplified results:

- **Option A**: \( 169^{52} \)
- **Option B**: \( 26^{52} \)
- **Option C**: \( 13^{52} \)
- **Option D**: \( 13^{24} \)

Each expression has been simplified using the exponent rules. If you need further steps or details, feel free to ask!