Question

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

16940
169 superscript 40 baseline

1340
13 superscript 40 baseline

16914
169 superscript 14 baseline

1314
13 superscript 14 baseline

Answer 1

To simplify the expression \( 1310 \cdot 134 \) using the Product Rule of Exponents, we can add the exponents of the same base, which is 13 in this case.

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

Here, we can rewrite the expression as:

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

So, the simplified expression is:

\[ 13^{14} \]

Thus, the correct response is:

**\( 13^{14} \)** (which corresponds to the option \( 1314 \)).