Question

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

1314
13 superscript 14 baseline

16914
169 superscript 14 baseline

16940
169 superscript 40 baseline

1340

Answer 1

To simplify the expression \( 1310 \cdot 134 \) using the Product Rule of Exponents, you need to add the exponents since the bases are the same.

According to the Product Rule of Exponents:
\[
a^m \cdot a^n = a^{m+n}
\]

In this case, we have:
\[
1310 \cdot 134 = 13^{10} \cdot 13^{4}
\]

Now, applying the Product Rule:
\[
13^{10} \cdot 13^{4} = 13^{10 + 4} = 13^{14}
\]

So the simplified expression is:
\[
13^{14}
\]

Thus, the correct response is:
**1314** or **13 superscript 14 baseline**.