Question

Use the Product Rule of Exponents to simplify the expression 1310 ⋅134
.(1 point)
Responses

16940
169 to the 40th power

16914
169 to the 14th power

1340
13 to the 40th power

1314

Answer 1

To simplify the expression \( 1310 \cdot 134 \) using the Product Rule of Exponents, we can first rewrite the bases with common bases.

The Product Rule of Exponents states that \( a^m \cdot a^n = a^{m+n} \).

Here, \( 1310 \) can be rewritten as \( 13^{10} \) and \( 134 \) can be rewritten as \( 13^4 \). Thus, the expression becomes:

\[
13^{10} \cdot 13^4
\]

Applying the Product Rule:

\[
13^{10 + 4} = 13^{14}
\]

So, the simplified expression is \( 13^{14} \).

Looking at the provided responses:

- **1314** (which is \( 13^{14} \)) is the correct answer.

Thus, the final answer is:

**1314**.